Combinations

Front

What is a combination?

Back

A combination is a selection of items from a larger set where the order of selection does not matter.

Front

How do you calculate combinations?

Back

The number of combinations of n items taken k at a time is calculated using the formula: C(n, k) = n! / (k!(n-k)!) where n! is the factorial of n.

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

What is the difference between permutations and combinations?

Back

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

Front

How many ways can you choose 3 items from a set of 5?

Back

C(5, 3) = 5! / (3!(5-3)!) = 10.

Front

If you have 10 different books, how many ways can you choose 2?

Back

C(10, 2) = 10! / (2!(10-2)!) = 45.

Front

What is the combination formula for selecting r items from n items?

Back

C(n, r) = n! / (r!(n-r)!)

Front

How many ways can you form a committee of 4 from 13 people?

Back

C(13, 4) = 13! / (4!(13-4)!) = 715.

Front

If a sandwich requires 3 meats from 6 options and 5 veggies from 10 options, how many combinations are there?

Back

C(6, 3) * C(10, 5) = 20 * 252 = 5040.

Front

How many ways can you select 3 courses from Group A, 1 from Group B, and 2 from Group C if Group A has 5 courses, Group B has 4, and Group C has 6?

Back

C(5, 3) * C(4, 1) * C(6, 2) = 10 * 4 * 15 = 600.