Question

homework 3.4: problem 2 (1 point) the 500 companies on the fortune 500 list include 55 companies that are based in new york and 24 companies with a female ceo. these include 4 companies that are both based in new york and have a female ceo. after graduation, erica wants to work for a fortune 500 company that is either based in new york or has a female ceo, or both. how many companies does she have to choose from?

Explanation:

Step1: Use the inclusion - exclusion principle

Let \(A\) be the set of companies based in New York and \(B\) be the set of companies with a female CEO. We know \(n(A) = 55\), \(n(B)=24\) and \(n(A\cap B)=4\). The formula for \(n(A\cup B)\) is \(n(A)+n(B)-n(A\cap B)\).

Step2: Substitute the values

Substitute \(n(A) = 55\), \(n(B)=24\) and \(n(A\cap B)=4\) into the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). So \(n(A\cup B)=55 + 24- 4\).

Step3: Calculate the result

\(55+24 - 4=75\).

Answer:

75