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Permutation & Combination : Overview & Practice Questions


Permutation is a way of arranging all the elements or members of a set into a sequence or arranged manner.

Combination is a way of selecting items from a collection, such that (unlike permutations) the order of selection does not matter. Combination refers to the combination of n things taken k at a time without repetition.

Permutation is often calculated by the given formula  

                                     Permutation and Combination Calculator

whereas, Combination is calculated by

                                                      Permutation and Combination Calculator

The relation between Permutation and Combination is as follows

                                          

PRACTICE PROBLEMS:

(1.) A group of 10 people who have never met are in a classroom. How many handshakes are exchanged if each pair shakes hands exactly once?

🔘15

🔘33

🔘45

🔘48

🔘120

Answer: 45

(2.) If the word “WOW” can be rearranged in exactly 3 ways (WOW, OWW, WWO), in how many ways can the word “MASSACHUSETTS” be rearranged? (Numeric Entry)

Answer: 64,864,800

 (3.) A polygon has 18 edges. How many different diagonals does it have? (A diagonal is a line drawn from one vertex to any other vertex inside the given shape. This line cannot touch or cross any of the edges of the shape. For example, a triangle has zero diagonals and a rectangle has two.)

🔘153

🔘175

🔘108

🔘120

🔘144

Answer: 153

(4.)  A student council is to be chosen from a class of 12 students consisting of a president, a vice president, and 3 committee members. How many such councils are possible?

🔘(12!)/7!*5!

🔘(12!)/7!*3!

🔘(12!)/5!*3!

🔘(12!)/7!

🔘12!

Answer: (12!)/7!*3!

(5.) An inventory of coins contains 100 different coins

Quantity A

Quantity B

The number of possible collections of 64 coins that can be selected where the order of the coins does not matter

The number of possible collections of 36 coins that can be selected where the order of the coins does not matter

 ðŸ”˜Quantity A is greater

🔘Quantity B is greater

🔘The two quantities are equal

🔘The relationship cannot be determined

Answer: The two quantities are equal

(6.) Seiko has a 6-sided number cube with sides labeled 1 through 6. If she rolls the cube twice, what is the probability that the product of the two rolls is less than 36?

🔘1/6

🔘1/3

🔘2/3

🔘5/6

🔘35/36

Answer: 35/36

(7.) Of 60 birds found in a certain location, 20 are songbirds and 23 are migratory. (It is possible for a songbird to be migratory, or not.)

Quantity A

Quantity B

The number of the 60 birds that are neither migratory nor songbirds

16

 ðŸ”˜Quantity A is greater

🔘Quantity B is greater

🔘The two quantities are equal

🔘The relationship cannot be determined

Answer: Quantity A is greater

(8.) At Lexington High School, everyone takes at least one language — Spanish, French, or Latin — but no one takes all three languages. If 160 students take Spanish, 70 take French, 80 take Latin, and 20 take exactly two languages, how many students are there?

🔘290

🔘200

🔘192

🔘164

🔘98

Answer: 290

(9.) Eight women and two men are available to serve on a committee. If three people are picked, what is the probability that the committee includes at least one man?

🔘1/32

🔘1/4

🔘2/5

🔘7/15

🔘8/15

Answer: 8/15

(10.) The probability of rain is 1/3 for every day next week. What is the chance that it rains on at least one day during the workweek (Monday through Friday)?

🔘1/2

🔘242/243

🔘63/64

🔘142/167

🔘56/27

Answer: 242/243

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