I go with BG: 98

I cant understand the logic of 96.

Here we go:

We need to select 3 ppl.

Option 1:

Choose 3 from 7 (No P or VP) - 7C3 = 35

Option 2:

P fills one of the positions - then VPs are out of question, hence 7C2 ways of choosing remaining 2 ppl from the 7. = 1C1 * 7C2 = 21

Option 3:

VPs fill one position, 2C1 & 7C2 fills the remaining 2 slots.

= 2C1 * 7C2 = 42

Hence 35+21+42 = 98.

Now coming to the 96 solution: It should be 98 too using the same explaination provided.

10C3 = 120 choose 3 out of 10

But the following cannot happen:

1. P + 2Vps = 1C1 * 2C2 = 1

2. P + 1 VP + 1 Other = 1C1 * 2C1 * 7C1 = 1 * 2 * 7 = 14

3. 2VPs + 1 Other = 2C2 * 7C1 = 1 * 7 = 7

So the total of above is 22

And 120 -22 = 98

The logic being used for 96 is:

Ways in which President is with vp = 1 (president) * 2(VP) * 8(others) = 16

Ways in which both VPs are together = 1 (vp) * 1 (vp) * 8 (others) = 8

8 is not a number to be considered at all. In any case the choice will be made between 1 P, 2 VP, 7 Others.

Cheers