Question

One professor grades homework by randomly choosing 5 out of 12 homework problems to grade. a) Andrew did only 5 problems of one assignment. What is the probability that the problems he did comprised the group that was selected to be graded

Answer 1

`Probability = (1)/(792)`

Explanation:

Given

`Questions = 12`

`Selection = 5`

Required

Probability of grading the selected 5 by Andrew

First, we need to determine the total number of selections.

This is calculated as:
`^(12)C_(5)`

Solving further:

`^(12)C_(5) = (12!)/((12-5)!5!)`

`^(12)C_(5) = (12!)/(7!5!)`

`^(12)C_(5) = (12*11*10*9*8*7!)/(7!*5*4*3*2*1)`

`^(12)C_(5) = (12*11*10*9*8)/(5*4*3*2*1)`

`^(12)C_(5) = (95040)/(120)`

`^(12)C_(5) =792`

There is only 1 for Andrew's question selection.

So, the required probability is:

`Probability = (1)/(792)`