Answer:
5.3%
Step-by-step explanation:
The final probability is calculated by means of the quotient of the specific combinations and the total of total combinations
Let's start with the specific ones,
First the number of combinations of 4 of the 30 students getting a spot, i.e .:
A combinations are equal to:
nCx = n! / x! * (n-x)!
Replacing:
30C4 = 30! / (4! * 26!) = 27405
Segundo the number of combinations of the other audience members filling the other 4 (8-4) spots n = 110, 140 - 30
110C4 = 110! / (4! * 106!) = 5773185
Now the total combinations of possible 8 contestants from the audience
140C8 = 140! / (8! * 132!) = 2.98 * 10 ^ 12
Finally, the probability is equal to:
P = (30C4 * 110C4) / 140C8
replacing:
P = 27405 * 5773185 / 2.98 * 10 ^ 12
P = 0.053
Therefore the probability is 5.3%
