Permutations & Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The number of permutations of n distinct objects is n! (n factorial).

Front

What is a combination?

Back

A combination is a selection of objects without regard to the order. The number of combinations of n objects taken r at a time is given by n! / (r!(n-r)!).

Front

How many ways can 10 players be arranged in a batting order?

Back

3628800 (10!)

Front

How many different ways can 6 classes be arranged in a school schedule?

Back

720 (6!)

Front

If there are 12 kinds of cookies, how many ways can 3 different kinds be chosen?

Back

220 (12 choose 3) = 12! / (3!(12-3)!)

Front

How many different outfits can be made with 5 pairs of pants, 9 shirts, and 6 ties?

Back

270 (5 * 9 * 6) = 270.

Front

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

Back

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

Front

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

Back

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

Front

If Erik can choose from 5 cake flavors, 7 icing flavors, and 3 topping flavors, how many cakes can he make?

Back

105 (5 * 7 * 3) = 105.

Front

What is the difference between permutations and combinations?

Back

Permutations consider the order of selection, while combinations do not.