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 difference between permutations and combinations?

Back

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

Front

If a stylist arranges 5 of 8 vases, how many arrangements are possible?

Back

6720 arrangements (calculated as P(8, 5) = 8! / (8 - 5)!).

Front

In how many ways can a team of 17 players choose 3 players?

Back

680 ways (calculated as C(17, 3) = 17! / (3! * (17 - 3)!)).

Front

What is an example of a situation that requires a permutation?

Back

Choosing a president and vice president from a group of candidates, where the order of selection matters.

Front

What is an example of a situation that requires a combination?

Back

Selecting members for a committee from a larger group, where the order of selection does not matter.

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.