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 many ways can you arrange 3 books on a shelf? (3 books)

Back

6 ways (3! = 3 × 2 × 1 = 6).

Front

How many ways can you choose 2 fruits from a selection of 5?

Back

10 ways (5 choose 2 = 5! / (2! × (5-2)!) = 10).

Front

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

Back

P(n, r) = n! / (n - r)!.

Front

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

Back

C(n, r) = n! / (r! × (n - r)!).

Front

If you have 5 different shirts, how many ways can you choose 3 shirts?

Back

10 ways (C(5, 3) = 5! / (3! × 2!) = 10).

Front

In how many ways can 4 students be arranged in a line?

Back

24 ways (4! = 4 × 3 × 2 × 1 = 24).