How many ways are there to walk from P to Q by only taking steps to the right or up?
We have two sets to consider
(right right up up up ) * ( right right right right up up up )
We have C(5,2) ways to select the positions for "right" in the first set and C (7,4) ways to select the positions for "right" in the second set
So....the total paths are C(5,2) * C(7,.4) = 10 * 35 = 350 possible paths
[ Note....the same result would be obtained by choosing any C(5,3) and C(7,3) positions for "up" in both sets ]
EDIT....THX TO THE GUESY FOR CATCHING MY ERROR !!!!