Question

evaluate the expression.
₁₁c₄
(1 point)
○ 5040
○ 3
○ 1980
○ 330

Explanation:

Step1: Recall the combination formula

The combination formula is \(_{n}C_{r}=\frac{n!}{r!(n - r)!}\), where \(n = 11\) and \(r=4\).

Step2: Calculate factorial values

\(n!=11! = 11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\), \(r!=4! = 4\times3\times2\times1\), \((n - r)!=(11 - 4)!=7! = 7\times6\times5\times4\times3\times2\times1\)
\(_{11}C_{4}=\frac{11!}{4!(11 - 4)!}=\frac{11!}{4!7!}=\frac{11\times10\times9\times8\times7!}{4\times3\times2\times1\times7!}\)

Step3: Simplify the expression

Cancel out the \(7!\) terms. Then \(\frac{11\times10\times9\times8}{4\times3\times2\times1}=\frac{11\times10\times9\times8}{24}\)
\(11\times10\times3\times1 = 330\)

Answer:

330