Unit 11 - 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 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 you have 3 shirts and 2 pairs of pants, how many outfits can you create?

Back

You can create 3 shirts * 2 pants = 6 different outfits.

Front

In how many ways can you arrange 5 books on a shelf?

Back

You can arrange 5 books in 5! = 120 ways.

Front

What is the difference between permutations and combinations?

Back

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

Front

How many ways can you select 3 fruits from a basket of 5 different fruits?

Back

You can select 3 fruits in C(5, 3) = 10 ways.

Front

If a committee of 4 is to be formed from 10 people, how many different committees can be formed?

Back

You can form 4-person committees in C(10, 4) = 210 ways.

Front

How many different license plates can be created with 3 letters followed by 4 digits?

Back

If letters can be repeated, there are 26^3 * 10^4 = 17,576,000 possible license plates.