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)!, 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 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

How many different arrangements can be made from the letters in the word 'BASKETBALL'?

Back

The number of arrangements is calculated as 10! / (2! * 2!) = 453600.

Front

If a pin code consists of 3 digits, how many different combinations can be formed using digits 0-9?

Back

There are 10 choices for each digit, so the total combinations are 10 × 10 × 10 = 1000.

Front

How many different cakes can Erik make if he chooses from 5 cake flavors, 7 icing flavors, and 3 topping flavors?

Back

The total combinations are 5 × 7 × 3 = 105.

Front

How many ways can a coach arrange a batting order for 10 players?

Back

The number of arrangements is 10! = 3628800.

Front

How many different three-course meals can Angela choose from 4 appetizers, 9 entrees, and 3 desserts?

Back

The total combinations are 4 × 9 × 3 = 108.