Combinations and Arrangements Problems

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 where the order does matter.

Front

How do you calculate the number of combinations of selecting r items from n items?

Back

The formula is 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 the number of permutations of selecting r items from n items?

Back

The formula is 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 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

How many ways can you arrange the letters in the word 'RHOMBUS'?

Back

The number of arrangements is 7! = 5040.

Front

If you have 5 people, how many ways can you select a president, vice president, and secretary?

Back

There are 5 choices for president, 4 for vice president, and 3 for secretary: 5 * 4 * 3 = 60.

Front

How many different pizzas can you create with 8 meats, 4 cheeses, 3 crust types, and 2 sauces?

Back

The total combinations are 8 * 4 * 3 * 2 = 192.

Front

How many ways can a coach choose 5 starting players from a team of 11?

Back

The number of ways is C(11, 5) = 462.

Front

What is the difference between a combination and a permutation?

Back

In a combination, the order does not matter; in a permutation, the order does matter.