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.

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 a DJ has 9 songs and chooses 3 to play, how many arrangements are possible?

Back

There are 504 ways to arrange 3 songs from 9.

Front

Is choosing songs a permutation or combination?

Back

It is a permutation because the order of the songs matters.

Front

What is the counting principle?

Back

The counting principle states that if there are m ways to do one thing and n ways to do another, then there are m * n ways to do both.

Front

How many ways can you order a car with 9 colors, 3 styles, and 2 sizes?

Back

There are 54 ways to order the car (9 * 3 * 2).

Front

What is the difference between permutations and combinations?

Back

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