how many ways can a history teacher choose 5 questions from a list of 8 study questions to be on the next…
how many ways can a history teacher choose 5 questions from a list of 8 study questions to be on the next test?
Answer
Answer:
56
Explanation:
Step1: Identify combination formula
The formula for combinations is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n$ is the total number of items, and $r$ is the number of items to be chosen.
Step2: Substitute values
Here, $n = 8$ and $r=5$. So $C(8,5)=\frac{8!}{5!(8 - 5)!}=\frac{8!}{5!3!}$.
Step3: Expand factorials
$8! = 8\times7\times6\times5!$, $3! = 3\times2\times1$. Then $C(8,5)=\frac{8\times7\times6\times5!}{5!\times3\times2\times1}$.
Step4: Simplify
The $5!$ terms cancel out. We have $\frac{8\times7\times6}{3\times2\times1}=\frac{336}{6}=56$.