# Thread: Difficult (for me, that is) Combinatorics/Probability problem

1. ## Difficult (for me, that is) Combinatorics/Probability problem

Four people are going for an interview between 9am and 10am. Each person is to be interviewed in two separate rooms for a total of 30 minutes. They are interviewed for 15 minutes in room 1. And they are interviewed for 15 minutes in room 2. Each person is interviewed by themselves (no doubling up occurs in a room in a specified time slot).

1) - How many ways can the interviews be scheduled during the one hour period.
2) - If a person arrives at 9am, what is the probability they will have their interviews consecutively (eg 1 at 9am, the other at 9:15.... or 1 at 9:30, the other at 9:45 etc...)
2) - If someone turns up at 9am, what is the probability they will be able to leave after the third interview since they need to attend another appointment somewhere else?

Any help with these ones will be greatly appreciated!!!

2. I believe the answer to 1 is:

$\displaystyle {{8}\choose{4,4}}=\frac{8!}{(4!)(4!)}=...$

This is because we are conducting 8 total interviews (numerator) in two rooms that have four slots each (denominator).

2 and 3 seem like you'd use the negative binomial distribution to solve.

3. Nopes I don't think so. There are more restrictions in the problem.
We need to use de-arrangement

4. So do you actually know how to do it? My friend and I tried to get it and we got 216.... For q1.... And 50% for the second answer. What do you think?

5. 216 is correct
Haven't tried Q2 Q3

6. How do you do question 1?

7. Room 1: Slot 1,2,3,4
Room 2: Slot 1,2,3,4

You can arrange 4 people to occupy Slot's in Room 1 in 4! ways
Once done, Slots in Room 2 can give given to 4 people, with care that no one occupies the same slot in both room 1 and room 2. This just de-arrangement for n = 4 which is equal to 9.
So 4!*9 is the ans

8. Thanks. I'm not familiar with the term "de-arrangement." I tried googling it but I'm not finding anything. Can you explain further?

9. Amen_cc clearly you have an idea on how to do this stuff (as opposed to me) any chance you could help a brother out and have a crack at the other questions.

10. Derangements are permutations of a set such that there is no element in it's original position. You need to use this in this problem because you can't have a person sitting in both 9:00 am timeslots etc. Google 'derangements' (not de arrangemnts) and you'll find a formula on wiki

11. Derangement - Wikipedia, the free encyclopedia
Plz look at this - it explains it pretty well

12. sure i will look at other questions as well

13. Originally Posted by aman_cc
sure i will look at other questions as well
Alright thanks heaps! Really appreciate it. Hope to hear from you soon

14. Come on peoples any help here would be MUCH appreicated

15. Can u plz explain Q2 and Q3 - I have not really followed them. Also it would be good if u cld share your working

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