Answer:
a) 7,858,539,612
b) 2,080,201,662
c) 346,700,277
d) 7,511,839,335
e) 410,040
Step-by-step explanation:
a. How many ways are there to extend the 6 offers to 6 of the 136 candidates?
Combinations of 136 (candidates) taken 6 (offers) at a time without repetition:
b. How many ways are there to extend the 6 offers to 6 of the 136 candidates, if we already know that Computer Joe is getting an offer, but we do not know which?
There are 6 ways Computer Joe can get an offer. Now there are left 5 offers and 135 candidates. So there are
6 times combinations of 135 taken 5 at a time without repetition:
c. How many ways are there to extend the 6 offers to 6 of the 136 candidates, if we already know that Computer Joe is getting an offer for job number 2?
Now, we only have 5 offers and 135 candidates. So there are combinations of 135 taken 5 at a time without repetition:
d. How many ways are there to extend the 6 offers to 6 of the 136 candidates, if we already know that Computer Joe is not getting any offers?
Here we have 6 offers and 135 candidates, given that Computer Joe is out. So there are combinations of 135 taken 6 at a time without repetition:
e. How many ways are there for 3 interviewers to select 3 resumes (one resume for each interviewer) from the pile of 136 resumes for the first interview round?
There are combinations of 136 taken 3 at a time without repetition:
![\large \binom{136}{3}=\frac{136!}{3!(136-3)!}=\frac{136!}{3!133!}=410,040](https://tex.z-dn.net/?f=%5Clarge%20%5Cbinom%7B136%7D%7B3%7D%3D%5Cfrac%7B136%21%7D%7B3%21%28136-3%29%21%7D%3D%5Cfrac%7B136%21%7D%7B3%21133%21%7D%3D410%2C040)