Question

what is the value of 9c4?
6561
3024
36
126

Explanation:

Step1: Recall combination formula

The combination formula is $_{n}C_{r}=\frac{n!}{r!(n - r)!}$, where $n = 9$ and $r=4$.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $9! = 9\times8\times7\times6\times5\times4\times3\times2\times1$, $4! = 4\times3\times2\times1$ and $(9 - 4)!=5!=5\times4\times3\times2\times1$. Then $_{9}C_{4}=\frac{9!}{4!(9 - 4)!}=\frac{9!}{4!5!}=\frac{9\times8\times7\times6\times5!}{4\times3\times2\times1\times5!}$.

Step3: Simplify the expression

Cancel out the $5!$ terms. $\frac{9\times8\times7\times6}{4\times3\times2\times1}=\frac{3024}{24}=126$.

Answer:

D. 126