What formula is used for this problem?
Evaluate
20!
18!
The "!" denotes the factorial of the number preceeding it. It is the product of
all the integers less than the number and greater than 1. By convention we take 0!=1.
So:
20!= 1x2x3x4x5...x18x19x20
18!= 1x2x3x4x5...x18.
So:
20!/18!=(1x2x3x4x5...x18x19x20)/(1x2x3x4x5...x18)=19x20=380
RonL
Well this is ambiguous there are plenty of possible meanings for this, but
I will assume you mean the binomial coefficient or combinations symbol:
$\displaystyle {11 \choose 3}$
also written:
$\displaystyle C^n_k$
This is defined to be:
$\displaystyle {n \choose k}=\frac{n!}{k!\,(n-k)!}$,
so in this case we have:
$\displaystyle {11 \choose 3}=\frac{11!}{3!\,8!}=\frac{11 \times 10\times 9}{3 \times 2 \times 1}=165$,
RonL