please make a significant effort to the problem and organized summary of the process you have followed and conclusions you can draw.

Question

Five applicants are to be scheduled for job interviews at five given times. On an application form, each applicant was asked to mark two out of the five times. What is the probability that each of them can be interviewed at one of the two times they have marked?

Answer 1

Each applicant has 5 choices, and they make these choices independently----thus the choices made be one are not related to the choices made by the other.

What is needed here is the probability that each applicant chooses the same 2 time slots. This can be found simply by noting that--once the first applicant's choices are made, the 2nd applicant sees 5 choices, including 2 "conflicts" which, if BOTH selected, means neither candidate will get an interview.

The odds of picking one conflict are 2/5. Once one slot is picked which is a conflict, then the remaining choices are 1 conflict out of 4 choices. Thus the odds of picking the second conflict is 1/4, and the combined odds are 2/5 * 1/4 = 1/10

This means the the probability of successfully scheduling the 2 interviews is 9/10 = 90%.