Permutation Questions and Answers

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A company's board of directors wants to form a committee of 3 of its members. There are 4 members to choose from. How many different committees of 3 members could possibly be formed?

There are 6 runners in a race. There will be a first - place and a second-place awarded. In how many different ways can the 2 prizes be awarded.

Suppose that a local area network requires eight letters for user names. Lower and uppercase letters are considered the same. How many user names are possible for the local area network?

(a) For a council consisting of 12 representatives, in how many ways can a president and a vice-president be selected? (b) How many ways are there to distribute 20 different books to five bookstores?

You have a well-shuffled 52-card deck. On average, how many pairs of adjacent cards are there such that both cards are red? (Adjacent cards meaning all combinations of 2 cards throughout the deck, so

How many permutations can be formed from 2n distinguishable objects and n distinguishable object? Provide a step-by-step solution.

Consider five coins labeled a, b, c, d, and e. Let x = the number of heads showing. (a) Manually count and tabulate all possible permutations for each of the following configurations: (i) x = 0 (ii)

What is the probability that a K-string over a set of size n forms a k-permutation? How does this question relate to the birthday paradox?

A grocery store is sponsoring a sales promotion where the cashiers give away one of the letters: A, E, L, S, U, V for each purchase. If the customer collects all six (spelling VALUES), he or she gets

Let n 4 be an integer and consider a uniformly random permutation of the set {1, 2, . . . , n}. Define the event A = "in the permutation, both 3 and 4 are to the left of both 1 and 2". Determine Pr(A)

Suppose Chuck, Sally, Linus, Lucy, Snoopy, Marcy, and Peppermint Patty are going to sit at a round table to play a game. How many different seating arrangements are there?

In a sweepstakes with nine hundred entries, the first winner selected receives the grand prize, the second receives first prize, and so on until all thirty prizes are awarded. How many possible outcom

A certain lock has three tumblers, and each tumbler can assume seven positions. How many different possibilities are there?

Six people are going to be seated in a row of 8 chairs. How many different ways may they be seated?

Three officers -- president, treasurer, and secretary -- are to be chosen from among four people: Ann, Bob, Cyd, and Dan. Bob is not qualified to be treasurer. Cyd's other commitments make it imposs

A club has 4 members. From these members, the positions of president, vice-president, and treasurer have to be filled. In how many different ways can these 3 positions be filled?

There are 12 students in a social studies class. Three students will be selected to present their term projects today. In how many different orders can three students be selected?

If your teacher tells you to do questions 6 through 19 in your math book for homework, how many questions is that?

An 8 space code is to be made from the 26 letters of the alphabet with repeats allowed. Find the probability that: a The code contains exactly two a's and no other repeats. b At least two spaces in th

For the following questions determine how many permutations (orderings) can be formed from {A, B, C, D, E} subject to the given constraints. Does not contain the substring AB nor CD (again directly,

Let an unbiased die be cast at random eight independent times. Find the conditional probability that each side appears at least once given that side z appears exactly twice.

How many ways are there to distribute five distinguishable objects into three indistinguishable boxes?

A warehouse tracks inventory using stock codes consisting of a sequence of 3 uppercase letters chosen from the list {A,B,C,D,E,F,G,H,J,K} followed by a sequence of 4 digits in the range {1 . . . 8}. H

How many different ways can seven people be seated around a table?

Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated (a) with no restrictions? (b) if each couple is to sit together? (c) if all the me

From a standard 52-card deck, how many 5-card hands consists of two-pair? (Two pair: two cards of one value, two cards of another value, and one other card.)

Six cards are drawn at random from a standard deck of cards. a. What is the probability of three of a kind, two of a kind and one other rank (i.e. the ranks of the cards are some aaabbc) b. What i

Compute P6,1. Compute C6,3. Compute C3,3.

How many ways are there to roll eight distinct dice so that all six faces appear?

1. Suppose repetitions are not allowed (a) Find the number n of three-digit numbers that can be formed from the six digits: 2,3,5,6,7,9. (b) How many of them are even? (C) How many of them excee

Ten members of a wedding party are lining up in a row for a photograph. a. How many ways are there to line up the 10 people? b. How many ways are there to line up the 10 people if the groom must b

a. To open a combination lock, you turn the dial to the right and stop at a number; then you turn it to the left and stop at a second number. Finally, you turn the dial back to the right and stop at a

For the following questions, find the number of (unordered) five-card poker hands, selecting from an ordinary 52-card deck, having the properties indicated. (a) Containing four of a kind, that is, fou

Six different cards are chosen at random from a standard 52 card deck (13 ranks/denominations in 4 suits). (a) What is the probability that there are three cards with one rank, two cards with another

In the game of "Between," two cards are dealt from a standard deck and not replaced. You then pick a third card from the deck. To win, you must pick a card that has a value between the other two cards

Three cards are picked at random from a deck of cards. What is the probability that the cards have successive numbers (they can belong to any suite). You can treat "Ace" as 1, "Jack" as 11, "Queen" a

Find the number of different ways to draw a 4-of-a-kind hand from a standard 52 card deck, i.e. X X X X Y where the X's are four cards of the same rank (A to 2) and Y differs from X in rank. (Note: th

A hand of 5 cards is drawn from 52 cards. Suppose that after you draw the first two cards, you see that they are the ace of spades and the 7 of spades. (a) The sample space is the same as in Problem

There are 5 guys (including Gomer) on Gomer's bowling team. After the beer frame they will each choose one of the following: a. Scud, b. Scud Lite, or c. Scud Ice. How many outcomes are possible?

A committee of 15 people consists of eight men and seven women. In how many ways can a subcommittee of five be form if the subcommittee consists of any five committee members?

Compute by formula: \begin{pmatrix} 9 \\ 5 \end{pmatrix} and _9P_5

In how many ways can a teacher arrange 10 students in the front row if there are 25 total students?

a. In how many ways 3boys and 3 girls sit in a row? b. How many ways 3 boys and 3 girls sit in a row if the boys and girls are each to sit together? c. How many ways if only boys sit together? d. How

(a) How many permutations of the letters TRIANGLE contain the strings AN and GL in order? (b) How many permutations of the letters TRIANGLE contain the letters ANG together (in order) as a unit? (c) H

A group contains n men and n women. How many ways are there to arrange these people in a row if the men and women alternate?

The Hawaiian alphabet (known as the piapa) was first written by 19th century missionaries and consists of 12 letters; the vowels A, E, I, O, and U, and the consonants H, K, L, M, N, P, and W. Assuming

An assembly operation for a computer circuit board consists of four operations that can be performed in any order. a) In how many ways can the assembly operation be performed? b) One of the operat

For the following questions determine how many permutations (orderings) can be formed from {A, B, C, D, E} subject to the given constraints. (a) The ordering contains the substring ACE (in that order

An orchestra has 2 violinists, 2 cellists, and 4 harpists. Assume that the players of each instrument have to sit together, but they can sit in their own group. In how many ways can the conductor sea

Let A = {1,2,3,4,5,6}. If f be a bijective function from A to A, then the no of such functions for which { f(k) \neq k } ,where k=1,2,3,4,5,6 is ?

A veterinarian assigned to a racetrack has received a tip that one or more of the 12 horses in the third race have been doped. She has time to test only 3 horses. How many ways are there to randomly

Suppose the 10 letters in the word R A N D O M N E S S were rearranged randomly. (a) What is the probability that the first four positions are occupied by the letters N and S? (b) What is the probabil

A friend of mine is giving a dinner party. His current wine supply includes 10 bottles of Zinfandel, 11 of merlot, and 8 of cabernet (he only drinks red wine), all from different wineries. (a) If he

If you have 15 CDs and only 5 slots to file them, what is the probability it can be done in alphabetical order?

Adam has 11 different CD's, of which 6 are pop music, 3 are jazz, and 2 are classical. How many different arrangements of all 11 CD's on the shelf are there if all the jazz CD's are separated?

The access code for a car's security system consists of four digits. The first digit cannot be 22 and the last digit must be even. How many different codes are available?

please do i Using all 8 letters, how many ways can we arrange the word SOFTWARE? In how many of the arrangements are the three vowels together? Using all 8 letters, how many ways can we arrange the wo

The color of a person's eyes is determined by a single pair of genes. Let B represent the dominant brown-eyed gene and b represent the recessive blue-eyed gene. Then, BB and Bb will all resu

One hundred people were asked. "Do you favor the death penalty?" Of the 33 that answered "yes" to the question, 14 were male. Of the 67 that answered "no" to the question, six were male. If one person

Assume that you are taking an eight-question true or false quiz. a. How many different ways are there to answer all eight questions? b. How many ways are there to get no questions wrong? How many wa

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