Combinations

Front

What is a combination?

Back

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

Front

How do you calculate combinations?

Back

The formula for combinations is C(n, r) = n! / (r!(n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.

Front

What is the difference between permutations and combinations?

Back

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

Front

If you have 5 colors and want to choose 2, how many combinations can you make?

Back

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

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 choose 3 students from a class of 10?

Back

C(10, 3) = 10! / (3!(10 - 3)!) = 120 ways.

Front

What is the combination of choosing all items from a set?

Back

Choosing all items from a set of n items is always 1 combination (C(n, n) = 1).

Front

In how many ways can you choose 4 books from a list of 10?

Back

C(10, 4) = 10! / (4!(10 - 4)!) = 210 ways.

Front

What is a real-life example of combinations?

Back

Choosing toppings for a pizza where the order of toppings does not matter.

Front

If you have 8 different fruits and want to choose 3, how many combinations can you make?

Back

C(8, 3) = 8! / (3!(8 - 3)!) = 56 combinations.