Question

The grade appeal process at a university requires that a jury be structured by selecting eight individuals randomly from a pool of eight students and nine faculty. What is the probability a jury of all students?

Answer 1

Probability:
`(1)/(24310)`

Explanation:

There are two methods:

1. Fraction method (Longer expression)

2. Combination method (Shorter expression)

Fraction method:

We want the numerator to be the number of students remaining and the denominator to be the total number of individuals (students + faculty) remaining after each selection.

`(8)/(17)*(7)/(16) *(6)/(15) *(5)/(14) *(4)/(13) *(3)/(12) *(2)/(11) *(1)/(10) = (1)/(24310)`

Multiplying the fractions mean they are in the same combination during one single selection process.

Combination method:

Most calculators should have a permutation and combination function. We will use combination as there is no specific order in selecting students.

`(8C8*9C0)/(17C8) = (1)/(24310)`

Pretend the C means "Choose", We want to choose all 8 students and 0 faculty, therefore "8 choose 8" for students and "9 choose 0" for faculty. Lastly divided by "17 (total individuals) choose 8 (students only)" to make it into a probability, similar to the fraction method but way shorter.