Question

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

Explanation:

Step1: Identify the 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

First, calculate \(n!=8! = 8\times7\times6\times5\times4\times3\times2\times1=40320\), \(r!=4! = 4\times3\times2\times1 = 24\), and \((n - r)!=(8 - 4)!=4! = 24\).

Step3: Substitute into the formula

\(C(8,4)=\frac{8!}{4!(8 - 4)!}=\frac{8\times7\times6\times5\times4!}{4!\times4!}=\frac{8\times7\times6\times5}{4\times3\times2\times1}\).
Simplify the fraction: \(\frac{8\times7\times6\times5}{4\times3\times2\times1}=\frac{1680}{24}=70\).

Answer:

70