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# Combinatorics

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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.

Feb 24, 2021

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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}\$.

Feb 24, 2021
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Thanks for the help!

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

Feb 24, 2021
edited by xXxTenTacion  Feb 24, 2021
edited by xXxTenTacion  Feb 24, 2021
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