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 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

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. For example, 5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

If there are 5 books, how many ways can you arrange them on a shelf?

Back

There are 5! = 120 ways to arrange 5 books.

Front

How many ways can you choose 3 students from a group of 10?

Back

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

Front

What is the difference between permutations and combinations?

Back

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

Front

If a pizza has 3 toppings, how many ways can you choose 2 toppings?

Back

Using combinations, C(3, 2) = 3 ways.

Front

How many different outfits can you make with 2 shirts and 3 pants?

Back

You can make 2 × 3 = 6 different outfits.