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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Tue Jul 30, 2013 10:35 am

a company has 13 employees, 8 of whom belong to the union. if 5 people work any one shift and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift ?

I dont have the asnwer choices, i just found it from BTG forum..

here is the link https://www.beatthegmat.com/combination- ... 66644.html

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Source: Beat The GMAT — Problem Solving | Tue Jul 30, 2013 10:35 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Jul 30, 2013 10:58 am

sana.noor wrote:a company has 13 employees, 8 of whom belong to the union. if 5 people work any one shift and the union contract specifies that at least 4 union members work each shift, then how many different combinations of employees might work any given shift ?

I dont have the asnwer choices, i just found it from BTG forum..
here is the link https://www.beatthegmat.com/combination- ... 66644.html

Of the 13 employees, 8 belong to the union, 5 do not.
Of the 5 workers selected, AT LEAST 4 must belong to the union.

Case 1: 4 union workers + 1 non-union worker
Number of ways to choose 4 union workers from 8 options = 8C4 = (8*7*6*5)/(4*3*2*1) = 70.
Number of ways to choose 1 non-union worker from 5 options = 5.
To combine these options, we multiply:
70*5 = 350.

Case 2: 5 union workers
Number of ways to choose 5 union workers from 8 options = 8C5 = (8*7*6*5*4)/(5*4*3*2*1) = 56.

Total options = 350+56 = 406.

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