Question

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

Answer 1

190578024 ways.

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}=(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}=(120!)/((120-5)!5!)`

`_(5)^(120)\textrm{C}=(120!)/(115!*5!)`

`_(5)^(120)\textrm{C}=(120*119*118*117*116*115!)/(115!*5*4*3*2*1)`

`_(5)^(120)\textrm{C}=(120*119*118*117*116)/(5*4*3*2*1)`

`_(5)^(120)\textrm{C}=(120*119*118*117*116)/(120*1)`

`_(5)^(120)\textrm{C}=(119*118*117*116)/(1)`

`_(5)^(120)\textrm{C}=(190578024)/(1)`

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