The formula for Combination is,
[tex]nCr=\frac{n!}{r!\left(n-r\right)!}[/tex]
Given
[tex]n=9,r=7[/tex]
Therefore,
[tex]^9C_7=\frac{9!}{7!\left(9-7\right)!}[/tex]
Simplify
[tex]\begin{gathered} \frac{9!}{7!\left(9-7\right)!}=\frac{9!}{7!(2!)}=\frac{9\times8\times7!}{7!2\times1}=\frac{9\times8}{2}=9\times4=36 \\ \therefore^9C_7=36 \end{gathered}[/tex]
The formula for Permutation is,
[tex]nPr=\frac{n!}{\left(n-r\right)!}[/tex]
Given:
[tex]n=9,r=7[/tex]
Therefore,
[tex]^9P_7=\frac{9!}{\left(9-7\right)!}[/tex]
Simplify
[tex]\begin{gathered} \frac{9!}{\left(9-7\right)!}=\frac{9!}{2!}=\frac{9\times8\times7\times6\times5\times4\times3\times2!}{2!}=9\times8\times7\times6\times5\times4\times3 \\ =181440 \\ \therefore^9P_7=181440 \end{gathered}[/tex]
Hence, there are 36 combinations and 181440 permutations.
