Permutations and Combinations

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

When do you use permutations?

Back

Use permutations when the arrangement or order of items is important.

Front

When do you use combinations?

Back

Use combinations when the arrangement or order of items is not important.

Front

Example of a permutation:

Back

Arranging 3 books on a shelf (A, B, C) can be done in 6 ways: ABC, ACB, BAC, BCA, CAB, CBA.

Front

Example of a combination:

Back

Choosing 2 fruits from a basket of 5 (apple, banana, cherry, date, elderberry) can be done in 10 ways.

Front

What is the formula for permutations of n items taken r at a time?

Back

The formula is P(n, r) = n! / (n - r)!.

Front

What is the formula for combinations of n items taken r at a time?

Back

The formula is C(n, r) = n! / [r!(n - r)!].

Front

How many ways can you arrange 4 students in a line?

Back

Using permutations: P(4, 4) = 4! = 24 ways.

Front

How many ways can you choose 3 students from a class of 10?

Back

Using combinations: C(10, 3) = 10! / (3!7!) = 120 ways.