Question

a stock analyst plans to include in her portfolio stocks from five of the 20 top - performing companies featured in a finance journal. in how many ways can she do this? question help: video ebook written example

Explanation:

Step1: Identify the problem type

This is a combination problem where we need to find the number of ways to choose 5 stocks from 20, which is a combination (since the order of selection doesn't matter). The formula for combinations is \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 20 \) and \( k = 5 \).

Step2: Calculate factorial values

First, recall that \( n!=n\times(n - 1)\times\cdots\times1 \). So, \( 20! = 20\times19\times18\times17\times16\times15! \), \( 5! = 5\times4\times3\times2\times1=120 \), and \( (20 - 5)!=15! \).

Step3: Substitute into the combination formula

Substitute \( n = 20 \) and \( k = 5 \) into \( C(n, k) \):

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Step4: Simplify the expression

Calculate the numerator: \( 20\times19\times18\times17\times16 = 1860480 \)
Calculate the denominator: \( 5\times4\times3\times2\times1=120 \)
Then, \( \frac{1860480}{120}=15504 \)

Answer:

15504