#1**+2 **

The possible set of paths from A to C is (R, R, U, U , U ) where R = Right and U = Up

But.....the"R's" can occupy any 2 of 5 places in the set

So......the number of paths from A to C = C(5, 2) = 10

Likewise....the set of possible paths from C to B is ( R, R, R, U)

And the "U" can occupy any 1 of 4 places

So.....the number of paths from C to B = C (4, 1) = 4

So.....the toal possible paths = 10 * 4 = 40

CPhill May 22, 2019