Question

Find the number C(10,6)

Answer 1

Answer:

210.

Step-by-step explanation:

Combination formula is

$nCr = \frac{n!}{r!(n-r)!}$

Then, we have that n = 10 and r=6:

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

$C(10,6) = \frac{10!}{6!4!}$

To simplify calculus, we are going to use that n! = (n-1)!n = (n-2)!(n-1)n and so on.

$C(10,6) = \frac{6!*7*8*9*10}{6!4!}$

$C(10,6) = \frac{7*8*9*10}{4!}$

$C(10,6) = \frac{5040}{4*3*2*1}$

$C(10,6) = \frac{5040}{24}$

$C(10,6) = 210.$