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

User BinW
by
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1 Answer

6 votes

Answer:

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.

User Dizzwave
by
7.9k points
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