FCP, Combinations, and Permutations

Front

What is a Permutation?

Back

A permutation is an arrangement of objects in a specific order. The order matters.

Front

What is a Combination?

Back

A combination is a selection of objects where the order does not matter.

Front

What is the Fundamental Counting Principle (FCP)?

Back

The Fundamental Counting Principle states that if one event can occur in 'm' ways and a second can occur independently in 'n' ways, then the two events can occur in m * n ways.

Front

When do you use Permutations?

Back

Use permutations when the order of selection is important.

Front

When do you use Combinations?

Back

Use combinations when the order of selection is not important.

Front

Example of a Permutation problem: How many ways can 3 runners finish in a race?

Back

The number of permutations of 3 runners is 3! = 6.

Front

Example of a Combination problem: How many ways can 2 students be chosen from a group of 5?

Back

The number of combinations is C(5,2) = 10.

Front

What is the formula for Permutations?

Back

The formula for permutations is P(n, r) = n! / (n - r)! where n is the total number of items and r is the number of items to arrange.

Front

What is the formula for Combinations?

Back

The formula for combinations is C(n, r) = n! / [r!(n - r)!] where n is the total number of items and r is the number of items to choose.

Front

If there are 5 different books, how many ways can you arrange 3 of them?

Back

Using permutations, the answer is P(5, 3) = 5! / (5 - 3)! = 60.