Question

I have some idea about how to solve this but I am not sure So please show your work

Answer 1

NPr=$\frac{n!}{(n-r)!}$
9P3=$\frac{9!}{(9-3)!}$=
9!/6!=(9*8*7*6*5*4*3*2*1)/(6*5*4*3*2*1) cancel=
(9*8*7)/(1)=504 ways


nCr=$\frac{n!}{r!(n-r)!}$
10C4=$\frac{10!}{4!(10-4)!}$=
$\frac{10!}{4!(6)!}$=
$\frac{10*9*8*7*6*5*4*3*2*1}{4*3*2*1*6*5*4*3*2*1}$, cancel=
$\frac{10*9*8*7}{4*3*2*1}$=
$\frac{2*5*3*3*2*4*7}{4*3*2*1}$=
$\frac{5*3*2*7}{1}$=210