Permutations and Combinations

Front

What is a permutation?

Back

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

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 instead of combinations?

Back

Use permutations when the order of selection is important.

Front

When do you use combinations instead of permutations?

Back

Use combinations when the order of selection is not important.

Front

How many ways can you arrange 5 books on a shelf?

Back

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

Front

How many ways can you choose 3 students from a class of 10?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

If you have 12 engineers, how many different teams of 4 can be formed?

Back

495 teams (12C4 = 495).

Front

How many ways can 18 runners finish in 1st, 2nd, and 3rd place?

Back

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