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QUESTION

How many different ways can you choose 3 vowels out of the box, if there are 5 vowels in the box and order does not matter?

10 different ways

There are 5 vowels and we need to take 3 and order does not matter. Therefore, this is a combination problem. For example, A, E, O, and E,O,A and O, E, A means the same

For combination

nCr=(n!)/((n-r)!*r!)

Let n=5 and r=3

nCr=(n!)/((n-r)!*r!)

5C3=(5!)/((5-3)!*3!)

5C3=10" "different ways

God bless...I hope the explanation is useful.