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

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Question 97167: Show that nC0+nC2+nC4+...=nC1+nC3+...=2^,where ^=n-1.
Click here to see answer by mathslover(157) About Me 

Question 97969: How many 5 letter code words can be formed from the letters in OUTFIELD if no letter is repeated and the last letter is a vowel? I don't know how to solve the problem and making the last letter a vowel, it's been irking me for a while. Any help will be appreciated!
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Question 97971: How many different automobile license plates can be made if each plate has a letter followed by three digits?
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Question 98302: NO.1.How many number are there which consist of seven figures(digits)?
NO.2How many numbers not more than fours digits can be formed with 7,8,9?
I need these answers,today.Please help me....

Click here to see answer by scott8148(6628) About Me 

Question 98520: How many 5 digit number exist between 10,500 and 11,000 if no digit may be repeated?
I answered 120 - 5x4x3x2x1 = 120 on a quiz and it was counted incorrect. The teacher said that the answer was 210 but did not explain what I did wrong. Help! I'm trying to study for the test now and I can't figure it out.

Click here to see answer by jim_thompson5910(35256) About Me 

Question 99010: A license consists of 1 letter followed by 1 digit followed by 1 digit followed by 3 letters. Assuming no resrictions, which expression shows how many licenses can be issued?
A- (26)(10)(25)(24)(23)
B- (26)(10)(25)(25)(25)
C- (26)(10)(26)(25)(24)
D- (26)(10)(26)(26)(26)
Thanks in advanced for anyone that helps.

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

Question 99083: Word problem - HELP!!
You have 15 paint colors to choose from. There are only four rooms in the house that need painting - in how many ways can you choose which color paint to use??
Makes no sense - help
Thanks

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Question 99374: Dont get this at all -
The variable Z varies jointly with x and y. Use the given values to write an equation relating x, y, and z. Then find Z when x = -4 and y = 7.
The equation would be z = kxy - right???
Now
x = 1, y = 1/3, z = 5
x = -6, y = 3, z = 2/5
Dont know what to do at all
HELP

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

Question 99923: The emergency room at Victory hospital employs eight male and ten female nurses. A special Triage unit of six nurses is being formed. In how many ways can this be done if:
a): The unit must have three males and three females?
b): The unit must have at least one female nurse?
Thanks...
Steve

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Question 102452: How many whole numbers between 1 and 100000 have addition of the digits equal the 6?
Thanks!

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Question 103080: How many ways can seven people be seated in a row if two of them refuse to sit next to each other?
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Question 102827: Determine the number of six-digit integers ( no leading zeros) in which the six-digit integer is i) even with no repetitions ii) divisible by 5 no repetitions.
For the 1st one I thought the last number could only be chosen in 5 ways
then that would leave 9 numbers to choose from. 1st number can't be 0 so it can be chosen in 8 ways leaving 8 numbers as the choice for the 3rd number 7 for the 4th 6 for the 5th number. I came up with 67,200 as the answer but the book has 68,880. Where did I go wrong?

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

Question 103736: i'm having trouble understanding what the formula should be for this problem/statement.
Three roses are to be placed in a vase. the color choices are red,pink,white,yellow, and orange. what is the probability that 3 roses selected at random will not include red?

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Question 103736: i'm having trouble understanding what the formula should be for this problem/statement.
Three roses are to be placed in a vase. the color choices are red,pink,white,yellow, and orange. what is the probability that 3 roses selected at random will not include red?

Click here to see answer by edjones(8007) About Me 

Question 103819: in how many ways can 4 boys and 2 girls be seated if
i)the 2 girls are to seat next to eachother
ii)the 2 girls are not to seat next to eachother

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Question 104927: Employee health care plans. A new employee has a choice of 5 health care plans,3 retirement plans, and 2 different expense accounts. If a person selects one of each option, how many different options does he or she have?
Click here to see answer by Fombitz(32388) About Me 

Question 105934: OK i need to work out the price that we were beaten by to win some jobs with a particular client.
I'll give 3 examples, and what I am after is a fixed formula so I can work out what was quoted by our opposition each time.
Example#1: We won the job, quoting $1550. The variation % is 0.00%
Example#2: We have lost this job. Our quote $590. Variation 100%, therefore I calculate the winning quote to be $295.
Example#3: Our Quote: $2145. Variation: 50% Would the winning quote be $1430?
Example#4: our quote: $2435. Variation: 35.12%
Example#5: Our quote $330. Variation: 65.0%
Can someone come up with a formula that works everytime?
Thanks Kathy

Click here to see answer by scott8148(6628) About Me 

Question 106501: The problem is :
Five computers are to be wired in a linear network, as in the following figure;
______ ______ ______ ______ ______
(Symbolizing five computers side by side)
How many permutations of the five computers are possible?
Thanks a lot for your help!!!

Click here to see answer by checkley75(3666) About Me 

Question 106508: The problem is:
A computer with an old processor locks up if more than 4 applications are running simultaneously. If the owner has 20 applications stored in his program file how many diferent sets of 4 can he run, so that his computer does not lock up?
Please help me. Thanks alot

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Question 106759: How many ways can a committe of 7 people be selected from a group of 15 people
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Question 107310: Please help with the following question:
A student is to answer 10 out of 15 exam questions.
a) how many choices has he if he must answer the first 2 questions?
b) how many choices has he if he must answer the first or second question but not both of them?
c) how many choices has he if he mush answer exactly three of the first five questions?
d) how many choices has he if he must answer at least three of the first five questions?
e) how many choices of question has he without restrictions?
Thanks a lot!

Click here to see answer by blc52877(2) About Me 

Question 108242: Simplify (5x^2y)(-4xy^2)(-x^3y^3) i would be very glad if you could answer this question it is for help on a paper we get for geometry called a CPR thank you for your help and i would appreciate an answer ASAP this CPR is due tomorrow Tuesday November 6th thank you
Click here to see answer by stanbon(75887) About Me 

Question 109090: How do you calculate the percentage of aluminum in an alloy while using NH as a constant to the formuls NH= (%Al/100 x 0.0556) + (%zn/100 x 0.0153). chapter-analysis of an aluminum-zinc alloy isbn-049501141

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Question 110244: 7X7 square consisting of 1x1 squares. How many different squares can be made inside the 7X7?
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Question 110283: 7X7 square consisting of 49 1x1 squares. How many total squares can be made (1x1, 2x2, 3x3, etc)
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Question 110661: In how many different ways can a panel of 12 jurors and 2 alternate jurors be chosen from a group of 28 prospective jurors
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Question 111638: how many permutations of the five computers are possible?
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Question 112442: how many different ways can someone arrange 8 books on a shelf?
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Question 112636: A. How many 10-digit phone numbers in the 972 area code have at least one repeated digit?
B. How many 7-digit phone numbers in the 972 area code have at least one 1 and at least one 3 among its digits?
Note: 0 or 1 can not be used as the first digit.

Click here to see answer by Edwin McCravy(20054) About Me 

Question 113745: You have a jar of red marbles and a jar of yellow marbles. You take several(any number you like) red marbles and transfer them to the yellow marble jar and mix them in. Then you randomly take the same number of marbles as you took before, but this time from the yellow(mixed)jar, and transfer them to the red jar. Which of the following is true?
a) there are now more red marbles in the yellow jar than there are yellow marbles in the red jar.
b)there are more yellow marbles in the red jar than there are red marbles in the yellow jar.
c)the number of reds in the yellow jar equals the number of yellows in the red jar.
Using either algebraic and diagram with word eexplanation, show why your choice of answers above is correct.

Click here to see answer by checkley71(8403) About Me 

Question 114638: I am so confused with this problem about Venn Diagrams, please help me.
----
Of 73 men, 54 wore belts, 20 wore suspenders, & 4 wore both.
How many wore ONLY a belt? Only suspenders? Niether?

---
I tried adding 54, 4 and 20. I got 78 and thats over 73 men. So, i subtracted 78 and 73 and got 5. That's 5 over the number of men total and if i subtract that from both belts and suspenders i would get less people wearing them. I'm so confused, please help me with this.
Thank you so much

Click here to see answer by scott8148(6628) About Me 

Question 115780: John Owns A HotDog Stand. His PRofit Is Represented By The Equation. P(x)= -x^2+10x+34, With P being profits and X the number of Hotdogs sold. What is the most he can earn? I think its an Inequality problem please some help me solve it
Click here to see answer by edjones(8007) About Me 

Question 115912: 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 of 10 (that is, it must end in 0)
(c) the telephone number must be a multiple of 100?
(d) the first 3 digits are 481
(e) no repetitions are allowed?

Click here to see answer by checkley71(8403) About Me 

Question 115913: If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 2 can be drawn in which both marbles are blue?
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Question 115910:
A couple has narrowed down the choice of a name for their new baby to 3 first names and 5 middle names. How many different first-and middle-name combinations are possible?

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Question 115975: From a pool of 7 secretaries, 3 are selected to be assigned to 3 managers, 1 secretary to each manager. In how many ways can this be done?
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Question 116189: the word problem is " Mosley Hills has reserved the digits 444, 445, and 446 as the prefixes for their phone number. How many different phone numbers are possible?
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Question 116189: the word problem is " Mosley Hills has reserved the digits 444, 445, and 446 as the prefixes for their phone number. How many different phone numbers are possible?
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Question 116296: Simplify:

-5(-3 + 8)

Click here to see answer by MathLover1(20849) About Me 

Question 116297: Simplify:
(-11)(-5)

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Question 117274: 7P(n,3) = 6P(n+1,3)
Not sure why the answer is n=20.

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Question 117767: How many two-letter permutations can be made from the letters L,M,N,O, and P?
How many three-letter combinations can be made from the letters in the word BLACK?




Thanks whoever helps me because I am totally confused.

Click here to see answer by jim_thompson5910(35256) About Me 

Question 117870: In how many ways 5 girls & 5 boys can be arranged if at least 2 girls sit together?
I know one method
10! - 5!x6!
but i want to it by another method so please help me for that

Click here to see answer by Edwin McCravy(20054) About Me 

Question 118127: Please help me with the following problem:
A poker hand consistes of 5 cards dealt from an ordinary deck of 52 playing cards.
a). How many poker hands are possible?
b). How many different hands consisting of three kings and two queens are possible?
c). The hand in part (b) is an example of a full house: 3 cards of one denomination and 2 of another. How many different full houses are possible?
d). Calculate the probability of being dealt a full house.
This is dealing with the counting rules and using the combination rule and the permutations rule.
Thank you for your help.

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

Question 118625: There are 12 teams in a curling competition. After the round-robin portion the 1st place teams plays the 4th place team and the 2nd place team plays the 3rd place team in the semi-finals. Determine the number of different possible pairings for the semifinal games. Explain your answer.
Any help would be appreciated. Thanks.

Click here to see answer by stanbon(75887) 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