Question

From a group of graduate students including 25 men and 22 women, 37 are chosen to participate in a presentation. What is the probability that exactly 19 men and 18 women are chosen

Answer 1

25.02% probability that exactly 19 men and 18 women are chosen

Explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the men and the women are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

`C_(n,x)` is the number of different combinations of x objects from a set of n elements, given by the following formula.

`C_(n,x) = (n!)/(x!(n-x)!)`

Desired outcomes:

19 men, from a set of 25

18 women, from a set of 22

`D = C_(25,19)*C_(22,18) = (25!)/(19!6!)*(22!)/(18!4!) = 1295486500`

Total outcomes:

37 people from a set of 25 + 22 = 47. So

`T = C_(47,37) = (47!)/(37!10!) = 5178066751`

Probability:

`p = (D)/(T) = (1295486500)/(5178066751) = 0.2502`

25.02% probability that exactly 19 men and 18 women are chosen