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. Only the group of objects is important.

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

The key difference is that permutations consider the order of selection, while combinations do not.

Front

If there are 5 positions to fill from 10 candidates, how many ways can this be done?

Back

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

Front

If a committee of 3 is to be formed from 10 people, how many different committees can be formed?

Back

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

Front

What is the factorial of a number?

Back

The factorial of a number n (denoted as n!) is the product of all positive integers up to n.

Front

Calculate the number of ways to choose 2 fruits from 5 different fruits.

Back

C(5, 2) = 5! / (2! * (5 - 2)!) = 10.

Front

Calculate the number of ways to arrange 4 books on a shelf from a collection of 6 books.

Back

P(6, 4) = 6! / (6 - 4)! = 360.