Permutations and Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters.

Front

What is a combination?

Back

A combination is a selection of objects where the order does not matter.

Front

When do you use permutations?

Back

Use permutations when the arrangement or order of items is important.

Front

When do you use combinations?

Back

Use combinations when the arrangement or order of items is not important.

Front

How do you calculate permutations of n items taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

How do you calculate combinations of n items taken r at a time?

Back

The formula is C(n, r) = n! / [r!(n - r)!].

Front

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n.

Front

Example of a permutation problem: How many ways can 3 students be arranged in a line?

Back

If there are 5 students, the answer is P(5, 3) = 5! / (5 - 3)! = 60.

Front

Example of a combination problem: How many ways can 3 students be chosen from a group of 5?

Back

The answer is C(5, 3) = 5! / [3!(5 - 3)!] = 10.

Front

What is the difference between permutations and combinations?

Back

Permutations consider order; combinations do not.