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

What is the formula for combinations?

Back

The formula for combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of items, and r is the number of items to choose.

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 6!

Back

720

Front

What is the difference between permutations and combinations?

Back

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

Front

What is the formula for permutations?

Back

The formula for permutations is P(n, r) = n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

Example of a permutation problem: How many ways can 3 students be arranged in a line from a group of 5?

Back

60 ways (P(5, 3) = 5! / (5 - 3)! = 60).

Front

Example of a combination problem: How many ways can 4 students be chosen from a group of 10?

Back

210 ways (C(10, 4) = 10! / (4! * (10 - 4)!) = 210).

Front

What does 'n choose r' mean?

Back

'n choose r' refers to the number of ways to choose r items from n items without regard to the order.