Question

15 candidates applied for a post in a company.In hoe many ways can 5 candidates be selected for the interview such that a particular candidate is always selected and another particular candidate is always rejected?

Answer 1

Answer:

$^{13}C_{4}$ ways.

Step-by-step explanation:

If a particular candidate is always rejected, simply don't count that person. (I feel sad for them though)

If a particular candidate is always selected, don't count the person AND reduce the number of open slots - because, one is already occupied, duh!

So now, we have 15 - 1 - 1 = 13 candidates, and 5 - 1 = 4 slots.

In mood for some C from PnC?

$^{13}C_{4}$ ways to select 4 out of 13 things, here, people.

(Also, please correct the question language at the beginning of the second sentence :))