Question

How to solve this hard probability question?

There are 16 students giving final presentations in your history course.

(a) Three students present per day. How many presentation orders are possible for the first day?

(b) Presentation subjects are based on the units of the course. Unit B is covered by three students, Unit C is covered by five students, and Units A and D are each covered by four students. How many presentation orders are possible when presentations on the same unit are indistinguishable from each other?

Answer 1

See below

Explanation:

a

On the first day, 16 students can go, 3 of which will go. We care about order (because persons A, B, then C presenting is different that persons C, B, then A) - so this is a permutation problem:

`P_(n,k)=(n!)/((n-k)!); n="population", k="picks"`

`P_(16,3)=(16!)/(13!)=16xx15xx14=3360` possbilities

b

Since the different units are indistinguishable, we in essence have 4 presentations to pick from. Each presentation type has at least as many presentations as are going to happen on day 1 (i.e. 3), and so what we can do is to look at the different presentation slots and choose a presentation unit.

For instance, there's the first presentation slot. We can have any one of the 4 different presentations, and so we have 4 choices.

Same for the second presentation slot. So that's another 4 choices.

And same for the third slot.

This gives:

`4^3=64`