Answer:
210.
Step-by-step explanation:
Combination formula is
[tex]nCr = \frac{n!}{r!(n-r)!}[/tex]
Then, we have that n = 10 and r=6:
[tex]C(10,6) = \frac{10!}{6!(10-6)!}[/tex]
[tex]C(10,6) = \frac{10!}{6!4!}[/tex]
To simplify calculus, we are going to use that n! = (n-1)!n = (n-2)!(n-1)n and so on.
[tex]C(10,6) = \frac{6!*7*8*9*10}{6!4!}[/tex]
[tex]C(10,6) = \frac{7*8*9*10}{4!}[/tex]
[tex]C(10,6) = \frac{5040}{4*3*2*1}[/tex]
[tex]C(10,6) = \frac{5040}{24}[/tex]
[tex]C(10,6) = 210.[/tex]
