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. 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 a team of 5 players is to be selected from a group of 10, how many combinations are possible?

Back

C(10, 5) = 10! / (5! * 5!) = 252.

Front

In how many ways can you arrange 3 books on a shelf if you have 5 different books?

Back

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

Front

What is the difference between permutations and combinations?

Back

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

Front

How many different 2 scoop sundaes can be made with 7 flavors of ice cream and 10 toppings?

Back

2,520 different sundaes can be made.

Front

How many ways can Rachel choose 3 different kinds of cookies from 12 kinds?

Back

There are 220 ways for Rachel to choose the cookies.