Permutations and 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 the formula n! / (r!(n-r)!).

Front

How do you calculate the number of ways to arrange n distinct objects?

Back

The number of ways to arrange n distinct objects is calculated using n! (n factorial).

Front

What is the value of 0! (zero factorial)?

Back

0! is defined to be 1.

Front

If you have 5 different books, how many ways can you arrange them on a shelf?

Back

The number of ways to arrange 5 different books is 5! = 120.

Front

How many ways can you choose 3 students from a group of 6?

Back

The number of ways to choose 3 students from 6 is given by the combination formula: 6! / (3!(6-3)!) = 20.

Front

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

Back

The formula for permutations of n objects taken r at a time 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 for combinations of n objects taken r at a time is C(n, r) = n! / (r!(n-r)!).

Front

In how many ways can you select 2 flavors from 10 ice cream flavors?

Back

The number of ways to select 2 flavors from 10 is C(10, 2) = 10! / (2!(10-2)!) = 45.

Front

If you have 4 different colors of paint, how many ways can you choose 2 colors?

Back

The number of ways to choose 2 colors from 4 is C(4, 2) = 4! / (2!(4-2)!) = 6.