Permutations and 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

How many ways can you arrange 3 books on a shelf?

Back

6 ways (3! = 3 x 2 x 1 = 6).

Front

If you have 5 different shirts, how many ways can you choose 2 shirts?

Back

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

Front

What is the difference between permutations and combinations?

Back

Permutations consider order; combinations do not.

Front

How many different 2-digit numbers can be formed using the digits 1, 2, 3, and 4 without repetition?

Back

12 different 2-digit numbers.

Front

In how many ways can a committee of 3 be formed from 10 members?

Back

120 ways (C(10, 3) = 10! / [3!(10 - 3)!]).