Calculating 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. It focuses on the group rather than the arrangement.

Front

How do you calculate permutations of n objects taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!, where n is the total number of objects and r is the number of objects to arrange.

Front

How do you calculate combinations of n objects taken r at a time?

Back

The formula is C(n, r) = n! / (r! * (n - r)!), where n is the total number of objects and r is the number of objects to choose.

Front

Solve: How many ways can you arrange 3 books on a shelf?

Back

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

Front

Solve: How many ways can you choose 2 fruits from 5 different fruits?

Back

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

Front

What is the difference between permutations and combinations?

Back

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

Front

If you have 4 different colored balls, how many ways can you arrange them?

Back

24 ways (4! = 4 x 3 x 2 x 1 = 24).

Front

If you have 10 students and want to select a president and a vice president, how many ways can you do this?

Back

90 ways (P(10, 2) = 10! / (10 - 2)! = 90).

Front

Solve: A committee of 3 is to be formed from 5 people. How many different committees can be formed?

Back

10 committees (C(5, 3) = 5! / (3! * 2!) = 10).