Permutation and combination

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 the number of 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 the number of 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

If a cafeteria has 2 salads, 3 entrees, and 2 beverages, how many meal combinations can be made?

Back

12 combinations (2 x 3 x 2 = 12).

Front

How many ways can 18 runners be placed in first, second, and third?

Back

4896 ways (P(18, 3) = 18! / (18 - 3)! = 18 x 17 x 16 = 4896).

Front

If there are 5 pairs of jeans, 8 t-shirts, and 2 pairs of shoes, how many outfits can be created?

Back

80 outfits (5 x 8 x 2 = 80).

Front

What is the difference between permutation and combination?

Back

Permutation considers the order of selection, while combination does not.

Front

In how many ways can a President, Vice-President, and Secretary be chosen from 12 people?

Back

This is a permutation problem because the order of selection matters.

Front

If a group of 14 people is taking an elevator in groups of 7, how many ways can they choose who goes on the second trip?

Back

This is a combination problem because the order of selection does not matter.