Question from Homework

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

 Question from Homework

    Do you see the Pascal's triangle ?

The number of paths form A to B that pass through C is \(\mathbf{10*4 = 40}\).