Combination Problem: C(70,67) = 54,740

[yakin]

How come the combination of C(70,67) is 54,740?

 

[MarkFL]

How come the combination of C(70,67) is 54,740?

The combination function is defined as:

$$C(n,r)={n \choose r}\equiv\frac{n!}{r!(n-r)!}$$

And so we have:

$${70 \choose 67}=\frac{70!}{67!(70-67)!}=\frac{70\cdot69\cdot68\cdot67!}{67!\cdot3!}=\frac{70\cdot69\cdot68}{3\cdot2}=35\cdot23\cdot68=54740$$