A club consists of 4 male students and 6 female students.The probability P(X) of selecting without replacement a sample of size 4 of 2 male students and 2 female students is
A)1/210
B)210/(6 15)
C)(6 15)/210
D)1/(6 15)

Question

Quizplus · Accepted Answer

The total number of ways to select a sample of 4 students from the club is given by the combination (10 choose 4):
(10 choose 4) = 10! / (4! * 6!) = 210

The number of ways to select 2 male students and 2 female students is given by the product of the combinations (4 choose 2) and (6 choose 2):
(4 choose 2) * (6 choose 2) = (4! / (2! * 2!)) * (6! / (2! * 4!)) = 6 * 15 = 90

Therefore, the probability of selecting a sample of 2 male students and 2 female students is:
P(X) = 90 / 210 = (6 15) / 210 = C The total number of ways to select a sample of 4 students from the 10 is (10 choose 4) = 210. 
The number of ways to select 2 male students from the 4 is (4 choose 2) = 6. 
The number of ways to select 2 female students from the 6 is (6 choose 2) = 15.
Therefore, the number of ways to select 2 male and 2 female students is 6*15 = 90. 
So, the probability of selecting this sample is 90/210 = 15/35 = 3/7. 
Simplifying this fraction, we get 6/14 = 3/7. 
So, the answer is C, (6 15)/210.

A Club Consists of 4 Male Students and 6 Female