Evaluate the factorial expression.
-$\frac { \mathrm { n } ! } { \mathrm { r } ! ( \mathrm { n } - \mathrm { r } ) ! }$, where $\mathrm { n } = 38$ and $\mathrm { r } = 9$
A) 50,616
B) 1406
C) $1,771,560$
D) $163,011,640$

Question

Quizplus · Accepted Answer

This expression is the formula for combinations, given by $C(n, r) = \frac{n!}{r!(n-r)!}$. It calculates the number of ways to choose $r$ elements out of $n$ without regard to the order. Substituting $n = 38$ and $r = 9$, we get $C(38, 9)$, which equals $163,011,640$.

Evaluate the Factorial Expression n!r!(n−r)!\frac { \mathrm { n } ! } { \mathrm { r } ! ( \mathrm { n } - \mathrm { r } ) ! }r!(n−r)!n!​

Evaluate the Factorial Expression $\frac { \mathrm { n } ! } { \mathrm { r } ! ( \mathrm { n } - \mathrm { r } ) ! }$