Question

What is the probability to choose three vowels from the letters a, b, c, d, e, f, g, h, i?

Answer 1

Answer;

`(1)/(84)`

Explanations;

Here, we want to calculate the probability of selecting 3 vowels from the given set

Mathematically, the probability of an event is the likelihood that an even will occur with values ranging between 0 and 1

Out of the giving letters, the vowels are a , e and i

The total number of letters in the set is 9

Now, out of the three vowels, we shall be selecting three, out of the 9 letters, we are selecting same 3

The number of ways we can select r items from a total n can be found using the combination formula below;

`^nC_r\text{ = }(n!)/((n-r)!r!)`

So, we simply want to divide the number of ways of selecting three out of three items, by the number of ways of selecting 3 out of 9 items

We can compute this as follows;

`(^3C_3)/(^9C_3)\text{ = }(1)/(84)`