+586 In the following grid, there are \(\binom{14}{9}\) paths of length 14 from A to B, where each step goes right or up.
(a)Find the number of these paths that pass through edge NO.
(b)Find the number of these paths that pass through edge PQ.
+605 a) $\binom{6}{1}=6$ ways to get to $N$ from $A$. $1$ way to get from $O$ to $B$. Ans: $\boxed{6}$
b) $\binom{9}{4}=126$ ways to get to $P$ from $A$. $\binom{3}{1}=3$ ways to get from $Q$ to $B$. Ans: $126*3=\boxed{378}$.
+586 Thanks for the help!
For b), I believe from Q to B there are 4c1=4 ways, bringing the total to 9c4 * 4c1 = 504.
