Combinations, Permutations, and Counting Principles

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

How do you calculate combinations?

Back

Combinations are calculated using the formula C(n, r) = n! / (r!(n - r)!), where n is the total number of items, and r is the number of items to choose.

Front

How do you calculate permutations?

Back

Permutations are calculated using the formula P(n, r) = n! / (n - r)!, where n is the total number of items, and r is the number of items to arrange.

Front

What does 10C4 represent?

Back

10C4 represents the number of ways to choose 4 items from a set of 10, without regard to the order.

Front

What does 10P4 represent?

Back

10P4 represents the number of ways to arrange 4 items out of a set of 10, where the order matters.

Front

In how many ways can you choose 3 players from a team of 17?

Back

The number of ways to choose 3 players from a team of 17 is calculated using combinations: C(17, 3) = 680.

Front

What is the difference between combinations and permutations?

Back

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

Front

What is the factorial of a number (n!)?

Back

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

Front

If you have 5 books, how many ways can you arrange them?

Back

You can arrange 5 books in 5! = 120 different ways.