Question

What would be an answer to: evaluate C(7,4)A) 35B) 210C) 5,040​

Answer 1

By definition, we have

$C(n,k) = \displaystyle \binom{n}{k}=\dfrac{n!}{k!(n-k)!}$

Where

$n! = n(n-1)(n-2)(n-3)\ldots 3\cdot 2$

So, in your case, we have

$C(7,4) = \displaystyle \binom{7}{4}=\dfrac{7!}{4!3!}=\dfrac{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2}{(4\cdot 3\cdot 2)\cdot (3\cdot 2)}=7\cdot 5=35$