How many paths are there from \(C\) to \(B\), if every step must be up or to the right?

Logic  Oct 19, 2018

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



cool cool cool

CPhill  Oct 19, 2018

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