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

Tutors Answer Your Questions about Permutations (FREE)

Question 943719: Suppose that 10 identical whiteboards are to be divided among 3 schools, SB, SPIA and IT, how many divisions are possible? How many if SB must receive at least 2 whiteboards.
Click here to see answer by Edwin McCravy(20055)

Question 944198: How many ways can 24 chairs be arranged in rows that have the same number of chairs?
Click here to see answer by stanbon(75887)

Question 944206: In a company, 55% of the workers are women. If 2,475 men work for the company, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
There

Click here to see answer by stanbon(75887)

Question 942879: a committee of four is selected from a group of 20 people.
if there are 10 women and 12 men in the group, how many different committees have a majority of men

Click here to see answer by Edwin McCravy(20055)

Question 943994: A two-stage experiment consists of first rolling a die and noting the number and then flipping a coin and noting heads or tails. How many outcomes are in the sample space?
Click here to see answer by Edwin McCravy(20055)

Question 943951: a computer password must be 5 characters long. the first character must be a capital letter. the second character must be a digit from 0 through 9, inclusive. the third character must be one of eight specified symbols. each of the fourth and fifth character can be any combination of capital or lowercase letters, digits or symbols. where the symbols are from the 8 specified symbols. how many different passwords can be made using these rules?
possible ans:
(A) 1,274,000
(B) 2,548,000
(C) 5,096,000
(D) 10,192,000
(E) 40,768,000
Click here to see answer by Edwin McCravy(20055)

Question 942788: Four persons are to be chosen at random from a group containing 3 men 2 woman and 4 children. Find the chance that exactly two of them are children.
Click here to see answer by Edwin McCravy(20055)

Question 943717: A committee of 10, consisting of 1 freshman, 2 sophomores, 4 juniors, and 3 seniors is to be chosen from a group of 5 freshmen, 6 sophomores, 3 juniors, and 4 seniors. How many committees are possible?
Click here to see answer by Edwin McCravy(20055)

Question 943250: Find the number of different combinations of four-person nominating committees that could be chosen from a class of 25 students
Click here to see answer by Edwin McCravy(20055)

Question 943193: A class consists of 12 girls and 18 boys. A president, vice-president and treasurer are chosen based on the number of votes. Find the probability of selecting a president, vice-president and treasurer where all 3 are different boys from the class.
Click here to see answer by Edwin McCravy(20055)

Question 942185: Q.3 Find a particular solution to the recurrence.
an+1 − 2an + an−1 = 5 + 2n, n � 1(15 marks) plz send full solution
Q.5 (a) If R = {(1, 1), (2, 1), (3, 2), (4, 3)}, find R2,R4.
(b) How many permutations are there of the letters, taken all at a
time, of the word ALLAHABAD?(7,7marks) plz send full solution
Q.6 Let A = {0, 1, 2, 3} and R = ((x, y) : x − y = 3k, k is an integer) i.e,
XRy if f x-y is divisible by 3, then prove that R is an equivalence
relation
Click here to see answer by Edwin McCravy(20055)

Question 944506: How many permutations of 3 digits (if they must be different) are there from the numbers 0-9?

Click here to see answer by dkppathak(439)

Question 944540: How many numbers are there each of 3 different digits if the first digit cannot be zero?
Click here to see answer by Edwin McCravy(20055)

Question 941398: What is the number of ways letters in the word KOMBINATOORIKA can be rearranged, such that no two consecutive letters are the same?
(the correct answer should be 710579520, not 100% sure though)
I tried first ordering 5 letters and then placing letters K in 6C2 ways, then A in 8C2 ways...etc, but with O-s it would make it different on when i select the three positions for them(whether 6C3,... or 6C2,8C2,11C3...), because i would need to multiply them at the end.
Also tried applying inclusion-exlcusion, but was unable to make it work.
Click here to see answer by Edwin McCravy(20055)

Question 944847: Out of 26 letters,
In how different many ways of five digit can be arranged???
Click here to see answer by Edwin McCravy(20055)

Question 944803: A total of 72 different two-item outfit permutations can be created from a pile of clothes containing
A. 2 garments
B. 8 garments
C. 9 garments
D. 10 garments
Click here to see answer by Edwin McCravy(20055)

Question 944504: (a) From the 13 albums released by a musician, the recording company wishes to release 9 in a boxed set. How many different boxed sets are possible?
(b) How many different committees of size 3 can be formed from 13 people?
This is the problem that I am working on. I was wondering how you determine which equation to use (the one for permutations or the one for combinations). The explanation for similar problems say that to use the permutation equation, the order does not need to matter. However, for the combination equations, the order does matter. So my question is, in a problem like the one stated above, how do you determine whether or not the order of the numbers matter?
Click here to see answer by Edwin McCravy(20055)

Question 944507: What is the sum of the first 10 terms of the arithmetic series {1, 4, 7, 10 ...}

Click here to see answer by Fombitz(32388)

Question 945087: In how many ways can 5 prizes be distributed among 4 boys when every boy can take one or more prizes?
Click here to see answer by Edwin McCravy(20055)

Question 945075: A roller coaster car has n rows of seats, each of which had room for two people. If n men and n women get into the car with a man and woman in each row, in how many different ways may the car be filled?
Click here to see answer by Edwin McCravy(20055)

Question 944984: Five different books will be displayed in the library window. How many different arrangement are there?
Click here to see answer by Fombitz(32388)

Question 945086: Q1:-In how many different ways is it possible to arrange the letter COMBINATIONS?
Q2:-In how many different ways can you choose a committiee of 5 members from a group of 20 people?

Click here to see answer by Edwin McCravy(20055)

Question 945000: In a free throw shooting contest, you shoot free throws until you miss once or until you make four shots. You keep track of the sequence of misses/makes. How many outcomes are in the sample space for this experiment?
Click here to see answer by Edwin McCravy(20055)

Question 945070: A boarding house has three bedrooms and 10 students. One bedroom has 1 bed, the second has 4 beds, and the third has 5 beds. In how many different ways can the students be assigned rooms?
Click here to see answer by Edwin McCravy(20055)

Question 945224: __8!___
2! (8-2)!. How does it equal 28
Click here to see answer by Fombitz(32388)

Question 945384: 1)A person has two sons and two daughters. There are three boys' schools and two girls' schools in the area where they lives.In how many different ways can the children be sent to school?In how many ways can the children be sent to school such that no two children attend the same school?
2)A shirt factory produces shirts of three different sizes. It is expected to produce shirts with two different materials and four different colors for the festive season. How many different shirts can be produced?
3)Find the number of all positive numbers with not more than four digits that can be made using the digits 0,1,2,3,4 and 5. Find also the number of numbers out of these in which each digit is not repeated.
Click here to see answer by Edwin McCravy(20055)

Question 945442: In how many different ways can you arrange nine CD's one after another on a shelf.
Click here to see answer by Fombitz(32388)

Question 944467: Find the number of ways in which the 7 letters of the word PYRAMID can be arranged in a row without restriction
Click here to see answer by Fombitz(32388)

Question 945376: A committee of 5 is to be chosen from 12 members of the Board of Directors, 3 of whom are accountants. How many ways can this done if at least two of the committee members must be accountant?

Click here to see answer by Edwin McCravy(20055)

Question 945243:
How many committees of four can be formed from 20 Republicans and 15 Democrats if at least one Republican and at least one Democrat must be on the committee?
Click here to see answer by Edwin McCravy(20055)

Question 945214: How many 8 digit numbers are there containing three 6s and five 2s?
Click here to see answer by Edwin McCravy(20055)

Question 945151: Suppose that three fair dice are thrown. Compute the probability of the following events:
(a) the event is �big�, that is, the sum of the three dice is at least 10 but the three dice
do not show the same value;
(b) the event that the sum is 13;
(c) the event that a specific combination of two different numbers appears, e.g. {3, 4}
appears.

Click here to see answer by Edwin McCravy(20055)

Question 945535: A company is composed of 5 senior executives, 10 executives and 5 senior managers. A 5 person committee is formed to attack a particular issue.
How many different 5 person committees are possible?
C(20,5) =20!/(20-5)!5!=(20!5*4*3*2*1)/15!=(20*19*18*17*16*15!)/(15!*5*4*3*2*1)=1860480/120=15504
If the committee must be composed of 2 senior executives, 2 executives and 1 senior manager, how many different 5 person committees are possible?

Click here to see answer by jim_thompson5910(35256)

Question 945526: 1)Alan has 5 pairs of trousers and 6 shirts. Ben has 7 pairs of trousers and 4 shirts. Who has the most choice of what to wear? Why?
2)From the digits 0, 1, 2, 3, 4, 5, how many 4-digit even numbers with distinct digits can be formed? (Hint: Consider two cases: when it begins with 1, 3 or 5 and when it begins with 2 or 4)

3)Morse code is made from dots and dashes. The letter E is a dot (using 1 character), the letter N is a dash followed by a dot (using 2 characters), the letter S is three dots (using 3 characters). Explain why it is possible to construct the 26 letters of the alphabet using maximum 4 characters.
4)5 cards are selected randomly from a packet of 52 cards (there are 4 suits in the packet, and each suit has 13 cards). In how many ways can at least 4 cards of the same suit be selected?

5)3 girls and 4 boys sit in a row for a photograph. Find the number of ways they can be seated if
(a) the 3 girls sit together.
(b) no girls sit together.
(c) only 2 of the girls sit together.
(d) the 3 girls sit in alphabetical order, from left to right, but not necessarily together.
(e) girls and boys alternate, where the tallest girl sits in the middle.

Click here to see answer by Edwin McCravy(20055)

Question 944565: A student has 5 engineering books, 3 math books, and 4 chemistry books. She is to put them all onto three shelves (top, middle, lower) with each shelf containing only books of a single discipline, but the order on any particular shelf is completely free. In how many ways can she do this ?
I'm stuck here, it seems easy enough, but why would the number of books matter if each shelf contains one discipline and the order on each shelf doesn't matter? Am I missing something here?
It looks along the lines of 5!*3!*4!*3!, but not sure.
Click here to see answer by Edwin McCravy(20055)

Question 940971: in how many distinguishable ways can 4 identical algebra books, 6 identical geometry books, 3 identical calculus books, and 5 identical discrete math books be arranged on a shelf
Click here to see answer by Edwin McCravy(20055)

Question 944709: From a group of six persons, how many committees of three can be formed if two of the six people cannot be on the same committee?
Click here to see answer by Edwin McCravy(20055)

Question 945542: Determine the term in Pascal's Triangle that these equations would lead you to:
Show ALL steps and explanations please, thank you.
Click here to see answer by Edwin McCravy(20055)

Question 945680: How many four digit numbers greater than 30000 can be formed with the digits 2,3,4 and 5 if no repetition are allowed

Click here to see answer by richard1234(7193)

Question 944541: In how many different ways can the letters of the word CALCULUS be arranged? How many of these arrangements begin and end with the same letter?
Click here to see answer by Edwin McCravy(20055)

Question 945682: There are 8 members of a club. Four members are to be chosen so that it contains A or B but not both. In how many ways can it be done?
Click here to see answer by Edwin McCravy(20055)

Question 945681: If 28C2r=24C2n-4=125:11 find r
Click here to see answer by Edwin McCravy(20055)

Question 945597: Solve the equation
where n is a natural number

Click here to see answer by Edwin McCravy(20055)

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