Permutations of n things taken r at a time is computed as follows:
[tex]\text{nPr}=\frac{n!}{(n-r)!}[/tex]Replacing with n = 9 and r = 3,
[tex]9P3=\frac{9!}{(9-3)!}=\frac{362880}{720}=504[/tex]Combinations of n things taken r at a time is computed as follows:
[tex]nCr=\frac{n!_{}}{(n-r)!\cdot r!}[/tex]Replacing with n = 10 and r = 7,
[tex]10C7=\frac{10!}{(10-7)!\cdot7!}=\frac{3628800}{6\cdot5040}=120[/tex]