Power Up Test 13

Front

What is a combination in mathematics?

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 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, r is the number of items to choose, and ! denotes factorial.

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 from 1 to n.

Front

If a teacher has 4 students and wants to choose 3, how many combinations are possible?

Back

There are 4 combinations possible.

Front

What is the difference between combinations and permutations?

Back

Combinations are selections where order does not matter, while permutations are arrangements where order does matter.

Front

What does 'n choose r' mean in combinatorics?

Back

'n choose r' refers to the number of ways to choose r items from a set of n items without regard to the order of selection.

Front

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

Back

You can make 10 combinations.

Front

What is the combination formula for choosing 2 from 5?

Back

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

Front

Can you give an example of a real-life situation where combinations are used?

Back

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

Front

What is the significance of combinations in probability?

Back

Combinations are used to calculate the likelihood of different outcomes when the order does not matter.