Question

Use the formula for n^C_r to evaluate the expression. 9^C_6

Answer 1

We need to evaluate the expression:

`_9C_6`

The formula for the combination is:

`_nC_r=(n!)/(r!(n-r)!)`

In this problem, we have:

`\begin{gathered} n=9 \\ r=6 \end{gathered}`

Thus, using the formula, we obtain:

`\begin{gathered} _9C_6=(9!)/(6!(9-6)!) \\ \\ _9C_6=\frac{9\cdot8\cdot7\cdot6!}{6!\text{ }3\cdot2\cdot1} \\ \\ _9C_6=(9)/(3)\cdot(8)/(2)\cdot7\cdot(6!)/(6!) \\ \\ _9C_6=3\cdot4\cdot7 \\ \\ _9C_6=84 \end{gathered}`

Therefore:

`_(9)C_(6)=84`