Question

How many ways can a committee of five be chosen from 120 employees to interview prospective applicants.

Answer 1

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.

$_{r}^{n}\textrm{C}=\frac{n!}{(n-r)!r!}$, 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:

$_{5}^{120}\textrm{C}=\frac{120!}{(120-5)!5!}$

$_{5}^{120}\textrm{C}=\frac{120!}{115!*5!}$

$_{5}^{120}\textrm{C}=\frac{120*119*118*117*116*115!}{115!*5*4*3*2*1}$

$_{5}^{120}\textrm{C}=\frac{120*119*118*117*116}{5*4*3*2*1}$

$_{5}^{120}\textrm{C}=\frac{120*119*118*117*116}{120*1}$

$_{5}^{120}\textrm{C}=\frac{119*118*117*116}{1}$

$_{5}^{120}\textrm{C}=\frac{190578024}{1}$

Therefore, the committee of five can be chosen from 120 employees in 190578024 ways.