Permutations & Combinations

Front

What is a permutation?

Back

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

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n.

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 x 4 x 3 x 2 x 1 = 120).

Front

In how many ways can you choose 3 fruits from a basket of 10?

Back

120 ways (C(10, 3) = 10! / (3! * 7!) = 120).

Front

What is the difference between permutations and combinations?

Back

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

Front

If you have 8 horses in a race, how many ways can you pick the first, second, and third place?

Back

336 ways (P(8, 3) = 8! / (8 - 3)! = 336).

Front

If you need to select 5 articles from 7, how many ways can you do this?

Back

21 ways (C(7, 5) = 7! / (5! * 2!) = 21).