Permutations & 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 the number of permutations of n objects taken r at a time?

Back

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

Front

How do you calculate the number of 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

Calculate 5!

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

What is the value of 0!

Back

0! = 1 by definition.

Front

If you have 10 books, how many ways can you choose 3 books?

Back

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

Front

How many different ways can you arrange 3 letters from the word 'CAT'?

Back

P(3, 3) = 3! = 6.

Front

What is the difference between permutations and combinations?

Back

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