how many ways can an investor select 4 mutual funds for his portfolio from a list of 8 recommended funds?

Answer:

70

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. Here, $n = 8$ and $r=4$.

Step2: Calculate factorial values

$n!=8!=8\times7\times6\times5\times4\times3\times2\times1$, $r!=4!=4\times3\times2\times1$, and $(n - r)!=(8 - 4)!=4!=4\times3\times2\times1$.

Step3: Substitute values into formula

$C(8,4)=\frac{8!}{4!(8 - 4)!}=\frac{8\times7\times6\times5\times4!}{4!\times4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}$.

Step4: Simplify the expression

$\frac{8\times7\times6\times5}{4\times3\times2\times1}=\frac{1680}{24}=70$.