15 selection bets

Considering that you asked the question 12 hours ago, I find strange that no one gave you the answer, are you fishing?
Everyone to busy ?

15 selections
10 folds = 3003
9 folds = 5005
8 folds = 6435

There`s a very simple way to work out all of these types of queries. It works for any number of `how many  x-folds from y selections`

In your example, you have 15 selections. So, start off by writing all the numbers, from 15 down to 1, across the page. This is the top half of the equation.
Next, (again, as in your example), you want to find out how many 8-folds there are. So, write, under the line, the numbers 8 down to 1.
Next, subtract the 8 from the 15, leaving 7. Alongside the 8 down to 1, write from 7 down to 1. Something like:

15,14,13,12,11,10,9,8,7,6,5,4,3,2,1
-----------------------------------
8,7,6,5,4,3,2,1,7,6,5,4,3,2,1


Next, cancel out any numbers that are both above and below the line, leaving you with:

15,14,13,12,11,10,9
-------------------
7,6,5,4,3,2,1


Insert multiplication signs:

15x14x13x12x11x10x9
-------------------
7x6x5x4x3x2x1

If you`re useless at maths, you can just calculate that out.

If you`re not altogether useless, it`s quicker to do a bit of cancelling. The 3x4 and the 2x5 cancelling the 12 and 10 leaves:

15x14x13x11x9
-------------
7x6x1

The 7 and the 14 become 1 and 2 leaving

15x2x13x11x9
------------
1x6x1


Cancelling15x2 over 6 leaves

5x13x11x9
---------   =6435 8-folds from 15 selections.
1



To find how many 9-folds, repeat the 15 to 1, but then do 9 to 1, and (15-9)=6 to 1

15x14x13x12x11x10x9x8x7x6x5x4x3x2x1
-----------------------------------
9x8x7x6x5x4x3x2x1x6x5x4x3x2x1

15x14x13x12x11x10
-----------------
6x5x4x3x2x1

15x14x13x11
-----------  =5005
6x1



For 10-folds, repeat, but have 10-1 and 5-1 under the line.


Really hoping this formats OK!