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