Answer:
190578024 ways.
Step-by-step explanation:
We are asked to find the number of ways in which a committee of 5 be chosen from 120 employees to interview prospective applicants.
We will use combinations to solve our given problem.
[tex]_{r}^{n}\textrm{C}=\frac{n!}{(n-r)!r!}[/tex], where,
n = Total number of items,
r = Number of items being chosen at a time.
Upon substituting our given values in above formula, we will get:
[tex]_{5}^{120}\textrm{C}=\frac{120!}{(120-5)!5!}[/tex]
[tex]_{5}^{120}\textrm{C}=\frac{120!}{115!*5!}[/tex]
[tex]_{5}^{120}\textrm{C}=\frac{120*119*118*117*116*115!}{115!*5*4*3*2*1}[/tex]
[tex]_{5}^{120}\textrm{C}=\frac{120*119*118*117*116}{5*4*3*2*1}[/tex]
[tex]_{5}^{120}\textrm{C}=\frac{120*119*118*117*116}{120*1}[/tex]
[tex]_{5}^{120}\textrm{C}=\frac{119*118*117*116}{1}[/tex]
[tex]_{5}^{120}\textrm{C}=\frac{190578024}{1}[/tex]
Therefore, the committee of five can be chosen from 120 employees in 190578024 ways.
