Question

What would be an answer to: evaluate C(7,4)

A) 35
B) 210
C) 5,040​

Answer 1

By definition, we have

`C(n,k) = \displaystyle \binom{n}{k}=(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}=(7!)/(4!3!)=(7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2)/((4\cdot 3\cdot 2)\cdot (3\cdot 2))=7\cdot 5=35`