Is there a quick way of finding how many combinations of 1/40 of a rectangle with 80 squares can be shaded?

Question

A line of 80 squares to have 1/40 shaded. What is the maximum number of ways this can be done. Is there a combination to work this out and if not does someone know the exact answer.
Thanks

Joe

Answer 1

1/40th of 80 squares is two squares. You need to shade two different squares. There are 80 choices for shading the first square. There are 79 choices for shading the second square (because one is already shaded).
You've also duplicated all possibilities twice. For instance, shade square 1 first then square 2. Or instead shade square 2 first then square 2. These are the same shaded squares but in different order.

The total number of possibilities is 80*79/2 = 3160

Answer 2

This is a classical case of combination. (where the order does not matter)
C(80,2)=P(80,2)/2!
=80*79/2
=3160