Question

The grade appeal process at a university requires that a jury be structured by selecting six individuals randomly from a pool of eleven students and thirteen faculty.​ (a) What is the probability of selecting a jury of all​ students? (b) What is the probability of selecting a jury of all​ faculty? (c) What is the probability of selecting a jury of two students and four ​faculty?

Answer 1

Answer: a)
`(3)/(874)`

b)
`(30)/(3059)`

c)
`(3575)/(12236)`

Explanation:

Given : Number of students : 11

Number of faculty members : 13

Total persons :
`11+13=24`

Total number of ways to structure a jury of six people from a group of 24 people :-

`^(24)C_(6)=(24!)/(6!(24-6)!)=134596`

a) Number of ways of selecting a jury of all​ students :-

`^(11)C_(6)=(11!)/(6!(11-6)!)=462`

Then , the probability of selecting a jury of all​ students :-

`(462)/(134596)=(3)/(874)`

b) Number of ways of selecting a jury of all​ faculty :-

`^(13)C_(6)=(13!)/(6!(13-6)!)=462`

Then , the probability of selecting a jury of all​ students :-

`(1716)/(134596)=(30)/(3059)`

c) Number of ways of selecting a jury of two students and four ​faculty :-

`^(11)C_(2)*^(13)C_(4)=(11!)/(2!(11-2)!)*(13!)/(4!(13-4)!)=39325`

Then , the probability of selecting a jury of all​ students :-

`(39325)/(134596)=(3575)/(12236)`