We need to evaluate the expression:
[tex]_9C_6[/tex]
The formula for the combination is:
[tex]_nC_r=\frac{n!}{r!(n-r)!}[/tex]
In this problem, we have:
[tex]\begin{gathered} n=9 \\ r=6 \end{gathered}[/tex]
Thus, using the formula, we obtain:
[tex]\begin{gathered} _9C_6=\frac{9!}{6!(9-6)!} \\ \\ _9C_6=\frac{9\cdot8\cdot7\cdot6!}{6!\text{ }3\cdot2\cdot1} \\ \\ _9C_6=\frac{9}{3}\cdot\frac{8}{2}\cdot7\cdot\frac{6!}{6!} \\ \\ _9C_6=3\cdot4\cdot7 \\ \\ _9C_6=84 \end{gathered}[/tex]
Therefore:
[tex]_{9}C_{6}=84[/tex]
