Question

I have some idea about how to solve this but I am not sure

So please show your work

Answer 1

nPr=
`(n!)/((n-r)!)`
9P3=
`(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=
`(n!)/(r!(n-r)!)`
10C4=
`(10!)/(4!(10-4)!)`=

`(10!)/(4!(6)!)`=

`(10*9*8*7*6*5*4*3*2*1)/(4*3*2*1*6*5*4*3*2*1)`, cancel=

`(10*9*8*7)/(4*3*2*1)`=

`(2*5*3*3*2*4*7)/(4*3*2*1)`=

`(5*3*2*7)/(1)`=210