Answer;
[tex]\frac{1}{84}[/tex]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;
[tex]^nC_r\text{ = }\frac{n!}{(n-r)!r!}[/tex]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;
[tex]\frac{^3C_3}{^9C_3}\text{ = }\frac{1}{84}[/tex]