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# The manager of a certain company gives its employees one rostered day

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5271
GMAT 1: 800 Q59 V59
GPA: 3.82
The manager of a certain company gives its employees one rostered day [#permalink]

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26 Dec 2017, 01:53
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Difficulty:

75% (hard)

Question Stats:

42% (01:09) correct 58% (01:01) wrong based on 45 sessions

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[GMAT math practice question]

The manager of a certain company gives its employees one rostered day off between Monday and Friday each week. In how many ways can four employees take their leave, if they cannot all be rostered off together?

A. $$120$$
B. $$125$$
C. $$620$$
D. $$625$$
E. $$3125$$
[Reveal] Spoiler: OA

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"Only $79 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" PS Forum Moderator Joined: 25 Feb 2013 Posts: 1059 Location: India GPA: 3.82 The manager of a certain company gives its employees one rostered day [#permalink] ### Show Tags 26 Dec 2017, 08:46 MathRevolution wrote: [GMAT math practice question] The manager of a certain company gives its employees one rostered day off between Monday and Friday each week. In how many ways can four employees take their leave, if they cannot all be rostered off together? A. $$120$$ B. $$125$$ C. $$620$$ D. $$625$$ E. $$3125$$ If there were no restriction on leave, then total number of ways 4 employees can take their leaves will be $$5*5*5*5=625$$ (each of the 4 employees has 5 options to choose from) Number of ways in which all the employees are on leave on the same day$$=5$$ ( everybody is on leave on Monday, Tuesday, Wednesday, Thursday or Friday) Hence number of ways in which leaves can be taken such that not all are restored off together$$=625-5=620$$ Option C Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5271 GMAT 1: 800 Q59 V59 GPA: 3.82 Re: The manager of a certain company gives its employees one rostered day [#permalink] ### Show Tags 28 Dec 2017, 00:32 => Each employee may be rostered off on $$5$$ different days. This gives $$5^4 = 625$$ ways in which they can take their rostered days off. We need to exclude the cases where are all employees take their leave together on Monday, Tuesday, Wednesday, Thursday or Friday. There are 5 such cases. So, the number of ways in which the four employees can take their leave is $$625 – 5 = 620$$. Therefore, the answer is C. Answer: C _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 3 month Online Course"
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Re: The manager of a certain company gives its employees one rostered day   [#permalink] 28 Dec 2017, 00:32
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