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 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 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 there are 5 books, how many ways can you arrange all of them?

Back

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

Front

If you have 10 different shirts, how many ways can you choose 2 shirts?

Back

45 ways (C(10, 2) = 10! / (2! * 8!) = 45).

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 arrange 3 out of 7 different colored balls?

Back

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

Front

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

Back

210 committees (C(10, 4) = 10! / (4! * 6!) = 210).

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.