Combinations & Permutations

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter.

Front

What is a permutation?

Back

A permutation is an arrangement of items from a larger set where the order does matter.

Front

How do you calculate combinations?

Back

The formula for combinations is C(n, r) = n! / (r!(n - r)!), where n is the total number of items, and r is the number of items to choose.

Front

How do you calculate permutations?

Back

The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

What is the difference between combinations and permutations?

Back

The key difference is that in combinations, the order of selection does not matter, while in permutations, the order does matter.

Front

If Rylan’s basketball team has 11 players, how many ways can his coach choose 5 starting players?

Back

462 ways (C(11, 5) = 11! / (5!(11 - 5)!) = 462).

Front

In a group of 14 people taking an elevator in groups of 7, is this a permutation or combination?

Back

This is a combination because the order of selection does not matter.

Front

How many ways can Rachel choose 3 different kinds of Girl Scout cookies from 12 kinds?

Back

220 ways (C(12, 3) = 12! / (3!(12 - 3)!) = 220).

Front

What is the probability that all 4 randomly picked students from a class of 5 boys and 2 girls are boys?

Back

1/7 (The probability is calculated as the number of ways to choose 4 boys from 5 divided by the total ways to choose 4 students from 7).

Front

How many possible ways are there to place 18 runners in first, second, and third?

Back

4896 ways (P(18, 3) = 18! / (18 - 3)! = 4896).