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

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Question 1070372: 5 girls and 4 boys sit in a row. If only two boys sit next to each other , find the number of
permutation.
Click here to see answer by Edwin McCravy(20054)

Question 1070731: Suppose that the functions g and h are defined as follows.

g(x) = 4/x, x is not 0
h(x) = x^2 -8
Find the compositions of g o g and h o h
simplify your answers as much as possible.
(g o g)( x) = _____
(h o h)(x) = ______
simplify your answer as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain).

Click here to see answer by rothauserc(4718)

Question 1070724: If NP2=90 , then find n

Click here to see answer by Edwin McCravy(20054)

Question 1070897: 1) 6 books are to be chosen from 8 different books
(i) Find the number of different selections of 6 books that could be made (ans 28)
A clock is to be displayed on a shelf with 3 of the 8 different books on each side of it. Find the number of ways this can be done if
(i) there are no restrictions in the choice of books (ans 20160
(ii) 3 of the eight books are music books which have to be kept together (ans 720)
Click here to see answer by KMST(5328)

Question 1070895: A security code is to be chosen using 6 of the following
the letters A,B,C
the numbers 2,3,5
the symbol *and $
i)Find the number of different security codes that many be chosen (Ans 20160)
ii) the security code are next to each other in the security code (Ans 3600)
Click here to see answer by Fombitz(32388)

Question 1071053: each of 25 pupils must choose 2 tasks from 5 possible tasks. Use the pigeonhole principle to show that at least three will choose the same task.
Click here to see answer by ikleyn(52776)

Question 1071142: Serial numbers for a product are to be made using
4
letters followed by
3
numbers. If the letters are to be taken from the first
6
letters of the alphabet with no repeats and the numbers are taken from the digits
0
through
9
with no repeats, how many serial numbers can be generated?

Click here to see answer by Fombitz(32388)

Question 1071130: 60% of the voters favor Ms. Stein. If 3 voters are chosen at�random, find the probability that all 3 voters support Ms. Stein.
Click here to see answer by Fombitz(32388)

Question 1071310: Can you please help me with this problem?
Consider a political discussion group consisting of 4 democrats, 7 republicans and 5 independents. Suppose that 2 group members are randomly selected in succession, to attend a political convention. Find the probability of selecting 2 independents.

Thank you

Click here to see answer by KMST(5328)

Question 1071225: A committee of 8 people is to be chosen from 7 men and 5 women.find the number of commitees that could be selected if the oldest man or the oldest woman,but not both must be included in committee. (ans 240)

Click here to see answer by Boreal(15235)

Question 1071247: Given Σ={A,B......,Z} and N={0,,.....,9}. A car license can be generated according to the following:
1) The length of license is 6.
2) A character in Σ takes the first position.
3) A character in Σ must be assigned to one of the position 3,4 or 5.
4) Any digit in N can be assigned to the last 5 positions.
5) Any digit in N occurring consecutively more than twice,like 555,6666 or 77777 is forbidden
How many car license are there
Click here to see answer by KMST(5328)

Question 1071388: A telephone number is composed of 8 digits starting with zero
How many subscribers we serve
Click here to see answer by Alan3354(69443)

Question 1071388: A telephone number is composed of 8 digits starting with zero
How many subscribers we serve
Click here to see answer by ikleyn(52776)

Question 1071464: In how many ways can 11 students be seated in their chairs so that exactly one seats on his or her own chair

Click here to see answer by ikleyn(52776)

Question 1071469: After ringing together 5 Bells begin to ring at intervals of 9 seconds, 6 seconds, 4 seconds, 10 seconds and 8 seconds respectively. How many times the Bells will ring together in one hour starting from first time ringing together?

Click here to see answer by ankor@dixie-net.com(22740)

Question 1071861: A student is to answer 10 out of 12 questions in an examination.
(a) How many choices she has?
(b) How many if she nust answer the first four questions
Click here to see answer by Boreal(15235)

Question 1071906: How many different sums of money you can make with four pennies, two nickels and four quarters?
Click here to see answer by ikleyn(52776)

Question 1072170: How many different 5 card hands can be dealt from a standard deck of 52 playing cards?
Click here to see answer by Edwin McCravy(20054)

Question 1072166: If a 4 digit combination has the numbers 3579 how many different combinations can there be?
Click here to see answer by Alan3354(69443)

Question 1072328: 2. Three cards are drawn from a standard deck w/out replacing them.
a.) what is the probability that they are all face cards?
b.) what is the probability that they are all from the same suit?
3. A pair of fair dice are rolled. Write down 6 by 6 sample space and find the probability that the sum of the #'s showing is 8 or 9.
4. 40% of the students in a school take English, 30% take math, and 25% take both math & English. A student is picked at random, what is the probability that they take Math or English?
Click here to see answer by stanbon(75887)

Question 1072165: A man, who works a five-day week, can travel to work on foot, by cycle or by bus. In how many ways can he arrange a week�s travelling to work?
Click here to see answer by Fombitz(32388)

Question 1072342: 5. In a manufacturing process for ball bearings, the mean diameter is 5mm with a standard deviation of 0.0002mm. Between what 2 measurements will 95% of all the diameters of all the ball bearings be found?
6. A game consists of tossing a coin & rolling a six sided die. The results can be recorded as follows: if a head shows up on the coin and a 4 shows up on the die, record this as H4. List the sample space for the results of the game.
7. A jar contains 5 red marbles & 4 blue marbles. 2 are drawn out at random (w/out replacing). Find the probability of getting 1 blue & 1 red marble in either order.
8. Exactly 1 of 3 contestants: John, Chris, or Andy will win the game show. The probability that John will win is 0.25, the probability that Chris will win is 0.65. What is the probability that Andy will win?
Click here to see answer by Boreal(15235)

Question 1072336: 1. 1000 tickets are sold for a charity lottery at $5 each. 3 numbers are drawn out at random to receive 1st, 2nd, 3rd place prizes of $2000, $1000, and $500 respectively. (Like 124, 321, & 996). What is the mean (expectation) from such a drawing?
2. A fair coin is flipped 6 times. What is is the probability of getting at least 2 heads? First figure out how many are in the sample space.
3. In a club there are 6 men & 8 women. A committee of four is to be chosen.
a.) how many possible committees are there?
b.) how many possible committees are there which have 2 men & 2 women?
4. A shipment of 100 DVD's has 5 which are defective. If you pick 2 at random (do not replace), what is the probability that they are all good (non defective)?

Click here to see answer by stanbon(75887)

Question 1072388: Assume that 2 cards are drawn from a standard 52-card deck. Find the following probabilities.
a) Assume the cards are drawn without replacement. Find the probability of drawing 2 face cards.
b) Assume the cards are drawn with replacement. Find the probability of drawing 2 face cards.
Click here to see answer by Alan3354(69443)

Question 1072407: how many distinct permutations can be formed from all the letters of the word SUCCESS

Click here to see answer by Edwin McCravy(20054)

Question 1072685: 3. You are about to be dealt a 5 card poker hand from a well shuffled deck
A. How many ways can you have a different 5 card hand
Click here to see answer by addingup(3677)

Question 1072850: What would be the probability that randomly choosing 3 states from the top 6 murder states would actually be the top 3 states for murders in the exact correct decreasing order (1. CA, 2. TX, 3. NY)?
Click here to see answer by Fombitz(32388)

Question 1072793: A committee of three people is selected at random from a set consisting of seven Americans, five French people, and three English people.
a. what is the probability of the event that that the committee consists of all Americans?
b. what is the probability of the event that the committee has no Americans?

Click here to see answer by jorel1380(3719)

Question 1072880: How many different 2-member tennis teams can be made from 7 students?
Click here to see answer by Alan3354(69443)

Question 1072879: A container contains 10 diesel engines. The company chooses 6 engines at random, and will not ship the container if any of the engines chosen are defective. Find the probability that a container will be shipped even though it contains 2 defectives if the sample size is 6.
Can someone please breakdown the steps to solve this. This is an online class and the help feature isn't explaining how to get the numbers needed to solve it. Thank you
Click here to see answer by KMST(5328)

Question 1072909: How many four-digit numbers can be formed using the digits 1,2,3,4,5,6,7,8, and 9.
a) if repetition is allowed?
b) if repetition is not allowed?
c) How many of 4 digits numbers in (a) are greater than 6000?

Click here to see answer by Fombitz(32388)

Question 1073140: A radio DJ is contractually obligated to run a commercial for Pepsi three times, a commercial for a local law firm once, and a new promo for the station twice per hour. in How many different ways can he do this?
Click here to see answer by Fombitz(32388)

Question 1073166: REIT, Inc. wants to build a complex consisting of a factory, office building, and warehouse. If the building contractor has 3 different kinds of factories, 2 different kinds of office buildings, and 4 different kinds of warehouses, how many models must be built to show all the possibilities to REIT, Inc?

Click here to see answer by Fombitz(32388)

Question 1073139: How many different code words can be made from the symbols *,*,*,@,@,#,#,#,#,$ if each word has 10 symbols?

Click here to see answer by KMST(5328)

Question 250270: find the term not involving y in the expansion of { 1/y^3 + y^2)^5
Pls explain- I am super lost my textbooks don't give me any questions like this.

Click here to see answer by MathTherapy(10551)

Question 1073327: Each ship in a fleet is assigned a three-digit number that does not begin with a 1 or a 0 and does not contain a 6 or a 9. How many different numbers may be assigned under these conditions.
Click here to see answer by jorel1380(3719)

Question 1073434: There are 10 points A,B... In a plane no three on the same line
1)how many lines are determined by the points?
2)how many of these lines do not pass through A or B ?
3)how many triangle are determined by the points ?
4)how many of these triangles contain the point A ?
5) how many of these triangles contain in side AB ?
Click here to see answer by KMST(5328)

Question 1073675: How many permutations are there for the word "routine".
Click here to see answer by ikleyn(52776)

Question 1073173: what is the soletion of in how many ways 7 man and 7 womenv can be seateted around table such that no two women can sit tgether
Click here to see answer by Edwin McCravy(20054)

Question 1074143: after ringing together 5 bales begin to ring at intervals of 9 seconds 6 seconds 4 seconds 10 seconds and 8 seconds respectively how many times the balls will ring together in one hour starting from first time ringing together

Click here to see answer by ikleyn(52776)

Question 1074314: find inverse of permutation (3 5 7 8) (2 3 1)
Click here to see answer by ikleyn(52776)

Question 1074322: find a word formed by using all the letters of the word
dhoni whose rank is 73?

Click here to see answer by Edwin McCravy(20054)

Question 1074170: 1. A student randomly answers the 7 questions on a multiple choice test.
Each question has 4 possible answers, only one of which is correct.
Would it be unlikely for the student to get all of the questions wrong?

Click here to see answer by Edwin McCravy(20054)

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