Question

a manufacturing company has 5 vice presidents: andrew, beth, charles, diane, and eric. their regional responsibilities are shown in the table. the president of the company wants to randomly select 2 of the 5 vice presidents to send to a conference. how many distinct groups of 2 vice presidents can be selected without replacement from this small population of 5 vice presidents? 2 4 5 10

Explanation:

Step1: Use combination formula

The combination formula is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 5\) (total number of vice - presidents) and \(r=2\) (number of vice - presidents to be selected).

Step2: Calculate factorial values

\(n!=5! = 5\times4\times3\times2\times1=120\), \(r!=2! = 2\times1 = 2\), \((n - r)!=(5 - 2)!=3! = 3\times2\times1=6\).

Step3: Substitute into the formula

\(C(5,2)=\frac{5!}{2!(5 - 2)!}=\frac{120}{2\times6}\).

Step4: Simplify the expression

\(\frac{120}{12}=10\).

Answer:

10