Permutations and Combinations

Front

What is a permutation?

Back

A permutation is an arrangement of objects in a specific order. The order of arrangement matters.

Front

What is a combination?

Back

A combination is a selection of objects where the order does not matter.

Front

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

Back

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

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)!].

Front

If you have 5 books and want to arrange them on a shelf, how many ways can you do this?

Back

120 ways (5! = 5 × 4 × 3 × 2 × 1 = 120).

Front

How many ways can you choose 2 fruits from a selection of 5?

Back

10 ways (C(5, 2) = 5! / [2!(5 - 2)!] = 10).

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 choose a president, vice president, and secretary from 10 students?

Back

720 ways (P(10, 3) = 10! / (10 - 3)! = 720).

Front

If a disc jockey has 7 songs and wants to play 3, how many arrangements can he make?

Back

210 arrangements (P(7, 3) = 7! / (7 - 3)! = 210).

Front

How many ways can you choose 3 desserts from 8 options?

Back

56 ways (C(8, 3) = 8! / [3!(8 - 3)!] = 56).