Combination vs. Permutation

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order does not matter.

Front

What is a permutation?

Back

A permutation is an arrangement of items from a larger set where the order does matter.

Front

When would you use combinations instead of permutations?

Back

Use combinations when the order of selection does not affect the outcome, such as picking team members.

Front

When would you use permutations instead of combinations?

Back

Use permutations when the order of arrangement is important, such as finishing positions in a race.

Front

How many ways can you choose 3 fruits from a basket of 5? (Order does not matter)

Back

This is a combination problem: C(5,3) = 10 ways.

Front

How many ways can you arrange 3 books from a set of 5? (Order matters)

Back

This is a permutation problem: P(5,3) = 60 ways.

Front

If you have 10 different shirts, how many ways can you choose 2 to wear?

Back

This is a combination problem: C(10,2) = 45 ways.

Front

If you have 10 different shirts, how many ways can you arrange all of them?

Back

This is a permutation problem: P(10,10) = 10! = 3,628,800 ways.

Front

What is the formula for combinations?

Back

C(n, r) = n! / (r!(n-r)!) where n is the total items and r is the items chosen.

Front

What is the formula for permutations?

Back

P(n, r) = n! / (n-r)! where n is the total items and r is the items arranged.