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.

Front

How many different three-digit PINs can be created using the digits 0-9?

Back

There are 1000 different three-digit PINs (000 to 999).

Front

How do you calculate the number of permutations of n objects taken r at a time?

Back

The formula is 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 the number of combinations of n objects taken r at a time?

Back

The formula is 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.

Front

Calculate 5! (5 factorial).

Back

5! = 5 × 4 × 3 × 2 × 1 = 120.

Front

If a basketball team has 11 players, how many ways can 5 players be chosen?

Back

There are 462 ways to choose 5 players from 11.

Front

How many different ways can 6 classes be arranged in a school day?

Back

There are 720 different ways to arrange 6 classes (6!).

Front

If Grant has 5 pairs of pants, 9 shirts, and 6 ties, how many different outfits can he make?

Back

Grant can make 270 different outfits (5 × 9 × 6 = 270).