Question

question evaluate the following combination. \\(\binom{16}{14}\\) give your answer as an integer. provide your answer below:

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 16$ and $k=14$.

Step2: Calculate $n - k$

$n - k=16 - 14=2$. So we need to find $C(16,14)=\frac{16!}{14!(16 - 14)!}=\frac{16!}{14!2!}$.

Step3: Expand factorials

Since $n!=n\times(n - 1)\times\cdots\times1$, $16! = 16\times15\times14!$ and $2! = 2\times1$. Then $\frac{16!}{14!2!}=\frac{16\times15\times14!}{14!\times2\times1}$.

Step4: Simplify the expression

The $14!$ terms in the numerator and denominator cancel out. We get $\frac{16\times15}{2\times1}=\frac{240}{2}=120$.

Answer:

120