Question

The grade appeal process at a university requires that a jury be structured by selecting 5 individuals randomly from a pool of 12 students and 5 faculty.

(a) What is the probability of selecting a jury of all students?

A) 1/792
B) 1/924
C) 1/7920
D) 1/11

Answer 1

The probability of selecting a jury of all students is 1/924, which is calculated by using combinations to divide the number of ways to choose 5 students from a pool of 12 by the number of ways to choose any 5 individuals from the total pool of 17. Option B is correct.

Step-by-step explanation:

The question asks about calculating the probability of selecting a jury of all students from a pool of 12 students and 5 faculty members when 5 individuals are to be chosen randomly. To find this probability, we use the combination formula to calculate the number of ways to select 5 students from 12 and divide this by the number of ways to select any 5 individuals from the total pool of 17 candidates (12 students + 5 faculty).

Probability of selecting 5 students = (Number of ways to choose 5 students from 12) / (Number of ways to choose 5 individuals from 17) = C(12,5) / C(17,5) = (12! / (5! * (12-5)!)) / (17! / (5! * (17-5)!)) = (792 / 6188) = 1/924, which is option B.