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

What is the difference between permutations and combinations?

Back

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

Front

If there are 5 positions to fill and 10 candidates, how many ways can you fill the positions?

Back

This is a permutation problem: P(10, 5) = 10! / (10 - 5)! = 30,240.

Front

If you need to choose 3 fruits from a basket of 10, how many combinations can you make?

Back

This is a combination problem: C(10, 3) = 10! / (3! * (10 - 3)!) = 120.

Front

In how many ways can you choose 10 players from a team of 13 for a game?

Back

C(13, 10) = 286.

Front

In how many ways can you arrange 4 runners from a group of 16 for a relay race?

Back

P(16, 4) = 16! / (16 - 4)! = 43,680.

Front

What is the significance of the factorial symbol (n!) in permutations and combinations?

Back

The factorial symbol (n!) represents the product of all positive integers up to n, used to calculate the total arrangements or selections.