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 a restaurant offers 4 appetizers, 9 entrees, and 3 desserts, how many different three-course meals can be made?

Back

108 different meals can be made (4 appetizers × 9 entrees × 3 desserts = 108).

Front

How many ways can Ashlyn choose 3 pies from 8 available pies?

Back

56 ways (C(8, 3) = 8! / (3! * 5!) = 56).

Front

How many ways can Rob's parents choose 4 siblings from 7 children?

Back

35 ways (C(7, 4) = 7! / (4! * 3!) = 35).

Front

How many ways can Andy choose 5 candy bars from 14 available?

Back

2002 ways (C(14, 5) = 14! / (5! * 9!) = 2002).

Front

How many ways can Rylan's coach choose 5 starting players from 11 players?

Back

462 ways (C(11, 5) = 11! / (5! * 6!) = 462).