+1206 How many paths are there from \(C\) to \(B\), if every step must be up or to the right?
+128475 To get from A to C we have this possible path
right up up
But we could select the "ups" to be in any two of the three positions
So C(3,2) = 3 possible paths from A to C
To get from C to B we have this possible path
right right right right up up
But we could select the "ups" to occupy any two of the six positions
So C(6,2) = 15 possible paths from C to B
So...the total possible paths from A to B = 3 * 15 = 45
