5.Find the number of paths from to that pass through point (Each step can only go up or to the right.)
Note that a set of moves that get us from A to C is just (R, R, U, U, U)
And we can choose any 2 of 5 places for R in the set and still get from A to C
So.....the total number of paths from A to C is C(5,2) = 10
Likewise
A set of moves that get us from C to B is just (U, R,R,R )
And we can choose any 1 of the 4 places for U in the set and still get from C to B
So....the the total paths from C to B is just C(4,1) = 4
And the total possible paths = C(5, 2) * C(4, 1) = 10 * 4 = 40