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 many ways can you arrange 3 prizes among 6 organizations?

Back

120 ways (calculated as 6P3 = 6!/(6-3)!)

Front

When do you use permutations instead of combinations?

Back

Use permutations when the order of selection is important.

Front

When do you use combinations instead of permutations?

Back

Use combinations when the order of selection is not important.

Front

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

Back

The formula is nPr = n! / (n - r)!.

Front

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

Back

The formula is nCr = n! / [r!(n - r)!].

Front

If you have 5 books and want to arrange them on a shelf, how many arrangements are possible?

Back

120 arrangements (calculated as 5! = 5 x 4 x 3 x 2 x 1).

Front

If you need to choose 3 flavors of ice cream from 10 available flavors, how many combinations can you make?

Back

120 combinations (calculated as 10C3 = 10! / [3!(10 - 3)!]).

Front

What is the difference between a permutation and a combination?

Back

The difference is that permutations consider the order of selection, while combinations do not.