Question

Question #acec1

Answer 1

Formula for combinations:
`C(n,r)=frac{n!}{r!(n-r)!}`

Let `n=10`, and let `r=6`

`C(10,6)=frac{10!}{6!(10-6)!}`

`=frac{10!}{6!*4!}`

`=frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1*4*3*2*1}`

`=frac{10*color(blue)(9)*color(green)(8)*7*cancel(6*5)*cancel(4*3*2*1)}{cancel(6*5)*color(green)(4)*color(blue)(3)*color(green)(2)*1*cancel(4*3*2*1)}`

`=frac{10*3*7}{1}`

`=210`