Questions on Algebra: Combinatorics and Permutations answered by real tutors!

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Question 170254: A couple has narrowed down the choice of a name for their new babyto 3 first names and 5 middle names. How many different first and middle name combinations are possible
Click here to see answer by checkley77(12844) About Me 

Question 170323: Find the term not involving y in the expansion of
bracket( 1 over y exponent 3 + y exponent 2 closed bracket) exponent 5

Click here to see answer by stanbon(75887) About Me 

Question 171588: Please find the middle term in the expansion of
(x/3 + 9y)^10

Click here to see answer by nerdybill(7384) About Me 

Question 171758: Please double check my work.
A musician plans to perform 4 selections. In how many ways can she arrange the musical selections?
4 * 4 = 16
4 * 3 = 12
4 * 2 = 8
4 * 1 = 4
I multiplied the answers all together and came up with 6,144 ways.
Did I do this right?

Click here to see answer by Alan3354(69443) About Me 

Question 171754: Please double check my work.
A bag contains 17 balls numbered 1 through 17. What are the odds in favor of selecting a ball that has an even number?
p(even) = 8/17
p(odd) = 9/17
so there is a 1/17 chance of selecting an even ball. Am I right?

Click here to see answer by Alan3354(69443) About Me 

Question 171961: How many ways can you sit seven people around a table made for seven?
Click here to see answer by edjones(8007) About Me 

Question 172778: The first three terms in the expansion of (1+ay)^n are 1,12y, and 68y^2
Evaluate a and n. Use the fact that:
(1+ay)^n=1+nay+n(n-1)/2(ay)^2+...
my teacher told me to use: c(n,k)(1)^n(ay)^k to figure it out and to refer to pascals triangle, But it hasnt helped. I would very much appricate if someone could help.
Thanks

Click here to see answer by vleith(2983) About Me 
Question 172778: The first three terms in the expansion of (1+ay)^n are 1,12y, and 68y^2
Evaluate a and n. Use the fact that:
(1+ay)^n=1+nay+n(n-1)/2(ay)^2+...
my teacher told me to use: c(n,k)(1)^n(ay)^k to figure it out and to refer to pascals triangle, But it hasnt helped. I would very much appricate if someone could help.
Thanks

Click here to see answer by adamchapman(301) About Me 

Question 173175: How many 7-digit telephone numbers are possible if the first digit cannot be zero and the 3 digits are 481
Click here to see answer by Alan3354(69443) About Me 

Question 173514: if the perimeter of a rectangle is 20 feet and the diagonal is 2 sqrt13 feet, then what are the length and width?
Click here to see answer by solver91311(24713) About Me 
Question 173514: if the perimeter of a rectangle is 20 feet and the diagonal is 2 sqrt13 feet, then what are the length and width?
Click here to see answer by Mathtut(3670) About Me 

Question 173860: sammy shopper is at the shell shop.the shop has brown shells and white shells.there are small,median,and large shells.list the possible combinations sammy may buy.
Click here to see answer by Fombitz(32388) About Me 

Question 173974: Hello,
I have worked out a story problem but I do not know if I am on the right track with it. Here is the problem:
The period T ( time in seconds for one complete cycle) of a simple pendulum is related tot he lenght L ( in feet) of the pendulum by the formula 8T^2=pie^2L. If a child is on a swing with a 10-ft chain, then how long does it take to complete one cycle of the swing?
This is how I worked it out:
T~2pie(46)
L is length of pendulum in meters
G is grauitational acceralation=9.8m/s.
10'=3.05m
t=2pie(l/G)
T=2pie (3.05/9.80=3.5 seconds is my answer

Click here to see answer by stanbon(75887) About Me 

Question 173995: area of a triangle. Find the exact are of a triangle with a base of sqrt30 meters and a height of sqrt6 meters
Click here to see answer by nerdybill(7384) About Me 

Question 174051: Hello,
Okay I have submitted this problem twice already but I believe that I have figured it out.
if the average radius of the orbit of venus is 0.723 AU, then how many years does it take for venus to complete one orbit of the sun? use these to figure the problem 28.46years 11.86 years sun to jupiter, 5.2AU
This is how I worked out the problem
v=x/.37793
jupiter11.86/5.2
5.2x=4.4822
x=.86 years to obrit the sun
for some reason that doesn't look right to me because how can you orbit the sun in .86 years is there a such thing?

Click here to see answer by stanbon(75887) About Me 
Question 174051: Hello,
Okay I have submitted this problem twice already but I believe that I have figured it out.
if the average radius of the orbit of venus is 0.723 AU, then how many years does it take for venus to complete one orbit of the sun? use these to figure the problem 28.46years 11.86 years sun to jupiter, 5.2AU
This is how I worked out the problem
v=x/.37793
jupiter11.86/5.2
5.2x=4.4822
x=.86 years to obrit the sun
for some reason that doesn't look right to me because how can you orbit the sun in .86 years is there a such thing?

Click here to see answer by vleith(2983) About Me 

Question 174216: Find the exact length of the side of a square whose digonal is 3 feet.
Click here to see answer by Mathtut(3670) About Me 

Question 174214: If a ball is tossed into the air from height of 6 feet with a velocity of 32 feet per second, then its altitude at time t ( in seconds) can be described by the fuction
A(t)=-16t^2+32t+6 Find the altitude of the ball at 2 seconds.
Now with this problem what I set this equation to zero?

Click here to see answer by vleith(2983) About Me 

Question 174213: If a manufacturer charges a q dollars each for footballs, then he can sell 300-150q footballs per week. Find a polynomial R(q) that represents the revenue if the price is $8.00 for each football.
Click here to see answer by Mathtut(3670) About Me 

Question 174238: n!
_______
2!(n-2)!
I understand that 5! is 5*4*3*2*1
I do not understand how to figure n!
I understand that 2! is 2*1 and (n-2)! is (n-2)*(n-1) which would make the problem
n!
________________
2*1(n-2)*(n-1)
Atleast I think that's what the problem would be, but now what? What do I do with the n! ??? I'm so confused. PLEASE HELP!! Thank you in advance!

Click here to see answer by Earlsdon(6294) About Me 
Question 174238: n!
_______
2!(n-2)!
I understand that 5! is 5*4*3*2*1
I do not understand how to figure n!
I understand that 2! is 2*1 and (n-2)! is (n-2)*(n-1) which would make the problem
n!
________________
2*1(n-2)*(n-1)
Atleast I think that's what the problem would be, but now what? What do I do with the n! ??? I'm so confused. PLEASE HELP!! Thank you in advance!

Click here to see answer by stanbon(75887) About Me 

Question 174215: Okay to make sure that I was on the right track witht his problem
Sketch the graph of each function or relation and state the domain and range.
y=|x|=-4
|x|-4=y
|x|=4+y
|x|=y+4
domain all real numbers range
x=+-(y+4)
x=y+4
x=-(y+4)
x=-y-4
x=y+4,-y-4
all real numbers and then to sketch the grapg wouldn't it come to like a v?

Click here to see answer by ilana(307) About Me 

Question 174518: Please help me :

find the total numbers of nine digit numbers which have all different digits.

Click here to see answer by josmiceli(19441) About Me 

Question 175180: Please help me on these questions, I've tried for hours and i'm torn. I beg you.
Solve each equation.
1. 2x3 – 5x2 – 3x + 2 = 2
2. x3 + 64 = 0
A. -4,2 +/- 2i/3
B. 3,-1 +/- 2i/3
C. -4,2 +/- 3i/4
D. 4,2 +/- 2i/3
3. x4 – 8x2 – 9 = 0
A. 2,-3,4i,i
B. -3,3,i,-i
C. 2,-3,4i,-i
D. 3,i,-i
Use the Rational Root Theorem to find all the roots of each equation.
4. x3 + 9x2 + 19x – 4 = 0
5. 2x3 – x2 + 10x – 5 = 0
6. Two roots of a polynomial equation with real coefficients are 2 + 3i and . Find two additional roots. Then find the degree of the polynomial.
A. 2-4i,-/8; Degree2
B. 2-3i,/7; Degree4
C. 2-3i,-/7;Degree4
D. 2+4i,-/9;Degree12
Evaluate each expression.
7. 6P4
8. 5(3P2)
9. 5C2 + 5C1
10. 7C3/7C4
11. There are 14 different types of boxed nails in the hardware store. You plan to buy 5 different types of boxed nails. How many different combinations are there?
12. In how many different orders can six colored blocks be chosen from a set of 23 different blocks?

Click here to see answer by solver91311(24713) About Me 

Question 175392: How many ways can you fill three different positions by choosing from 15 different people? I keep getting 15 3.
Click here to see answer by Alan3354(69443) About Me 

Question 175397: How do I solve the inequality -4y+6<-14?
Click here to see answer by Mathtut(3670) About Me 

Question 175396: What inequality sign would make a true statement if it replaced the question mark in the following equation: 3-5?-3
Click here to see answer by Mathtut(3670) About Me 

Question 175407: How many ways can you arrange eight books on a shelf?
Click here to see answer by rapaljer(4671) About Me 

Question 175406: How many arrangements of the letters in the word 'olive' can you make if each arrangement must use three letters?
Click here to see answer by stanbon(75887) About Me 

Question 175405: If (base 100)C(base 2) has a value of 4,950, what is the value of (base 100)C (base98)?
Click here to see answer by rapaljer(4671) About Me 

Question 175401: Please help, I'm gettin no where with it. Car thieves steal on automobile out of 400 of a certain type every year in a certain city. What annual net premium should an owner pay for theft insurance in the amount of $16,000 on the certain type of car?
Click here to see answer by stanbon(75887) About Me 

Question 175399: Please help me solve the problem: A teacher has a set of 12 problems to use on a math exam. The teacher makes different versions of the exam by putting 10 questions on each exam. How many different exams can the teacher make?
Click here to see answer by gonzo(654) About Me 

Question 175393: How many different permutations can you make with the letters in the word seventeen?
Click here to see answer by gonzo(654) About Me 
Question 175393: How many different permutations can you make with the letters in the word seventeen?
Click here to see answer by Edwin McCravy(20054) About Me 

Question 176287: 6!
Click here to see answer by EMStelley(208) About Me 

Question 170668: : 1.how many 7-digit telephone numbers are possible if the first digit cannot be 0 and
a: only odd digits may be used.
b: the telephone number must be a multiple 0f 10
c: the telephone number must be a multiple of 100
d: the 1st 3 digits are 481
e: no repetition are allowed.This question is from textbook
: 1.how many 7-digit telephone numbers are possible if the first digit cannot be 0 and
a: only odd digits may be used.
b: the telephone number must be a multiple 0f 10
c: the telephone number must be a multiple of 100
d: the 1st 3 digits are 481
e: no repetition are allowed.

Click here to see answer by EMStelley(208) About Me 

Question 176545: Please Help me solve this question: A particular website requires that users select a password with between 6 and 8 characters (inclusive). Each character can be a lower case letter, an upper case letter, or one of the digits 0,1,2,...,9. A password must start with a letter, and must have at least one digit. A sample password is tIc4SS. How many such passwords are possible.
Thanks

Click here to see answer by Fombitz(32388) About Me 

Question 176974: Find n so that nC3=nP2
Click here to see answer by stanbon(75887) About Me 

Question 176989: An auditorium has 50 rows of seats. The first row has 20 seats, the second has 21, each row having 1 more seat than the previous. How many seats are there together?
(I figured it out by multiplying 50x20, and then adding the product with the sum of 49+48..., but I do not know a short cut or formula to get the answer)

Click here to see answer by solver91311(24713) About Me 

Question 176991: A club consists of 25 married couples. Determine how many ways a committee of 7 people can be formed from these couples if
a) there are no restrictions?
b) there are exactly 5 men on the committe?
c) at least one person must be a man?
d)there must be at least 3 women and at least 2 men?: A club consists of 25 married couples. Determine how many ways a committee of 7 people can be formed from these couples if
d)there must be at least 3 women and at least 2 men?

Click here to see answer by stanbon(75887) About Me 

Question 177533: 1) The flow of heat (Q) through a material is given by Q = (K.A.O.)/ d
a) Transpose the formula to make A the subject.
b) find the value of A if Q = 300, O = 40 , d = 0.5 and K = 24

Click here to see answer by stanbon(75887) About Me 

Question 179113: Please you help me solve these question.
How do you know?
6.)Members from 6 different school organizations decorated floats for the homecoming parade. How many different ways can first,second, and third prize be awarded?
8.)Gregory has a coupon for $1 off the purchase of 3 boxes of Munchie brand cereal. The store has 5 different varieties of Munchie brand cereal. How many ways can Gregory choose 3 boxes of cereal so that each boz is a different variety?
Please rely me back as soon as you could.
Thank you so much.

Click here to see answer by stanbon(75887) About Me 

Question 179123: Please you help me fins this problem
How do you know?
15.) What if...? In the United Kingdom's National Lottery, you must correctly select a group of 6 numbers from 49. Suppose that the contest were changed to selecting 7 numbers. How many more ways would there be to select the number?
Please rely me back as soon as you could.
Thank you.

Click here to see answer by edjones(8007) About Me 
Question 179123: Please you help me fins this problem
How do you know?
15.) What if...? In the United Kingdom's National Lottery, you must correctly select a group of 6 numbers from 49. Suppose that the contest were changed to selecting 7 numbers. How many more ways would there be to select the number?
Please rely me back as soon as you could.
Thank you.

Click here to see answer by Mathtut(3670) About Me 

Question 179120: How many 6P6 and 5C5 are there?
How do you know?
thank you.

Click here to see answer by Mathtut(3670) About Me 

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035