Permutations Vs. 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 many ways can 5 people be arranged in a line?

Back

120 ways (5! = 5 x 4 x 3 x 2 x 1 = 120).

Front

In a race, how many ways can 3 runners finish in 1st, 2nd, and 3rd place?

Back

6 ways (3! = 3 x 2 x 1 = 6).

Front

If you have 10 books and want to choose 3 to read, how many combinations are there?

Back

120 combinations (10C3 = 10! / (3!(10-3)!) = 120).

Front

What is the formula for permutations of n items taken r at a time?

Back

nPr = n! / (n - r)!.

Front

What is the formula for combinations of n items taken r at a time?

Back

nCr = n! / (r!(n - r)!).

Front

Example of a permutation problem: How many different ways can the letters A, B, and C be arranged?

Back

6 ways (ABC, ACB, BAC, BCA, CAB, CBA).