Calculating 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

Solve: How many ways can 3 team captains be chosen from 8 seniors?

Back

56

Front

Solve: How many ways can 10 players be chosen from 13?

Back

286

Front

What is the difference between permutations and combinations?

Back

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

Front

In a relay race, if the order of runners matters, what do we use?

Back

Permutation.

Front

In a competition where the top 3 finishers are awarded medals, what do we use to calculate the arrangements?

Back

Permutation.

Front

If you are selecting a committee where the order of members does not matter, what do we use?

Back

Combination.