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.

xXxTenTacion Feb 24, 2021

#1**+2 **

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: $126*3=\boxed{378}$.

thedudemanguyperson Feb 24, 2021

#2**0 **

Thanks for the help!

For b), I believe from Q to B there are 4c1=4 ways, bringing the total to 9c4 * 4c1 = 504.

xXxTenTacion Feb 24, 2021