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An executive is planning his morning schedule,which will include five

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An executive is planning his morning schedule,which will include five  [#permalink]

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New post Updated on: 05 Aug 2019, 06:53
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Question Stats:

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An executive is planning his morning schedule, which will include five meetings, three of which are with Human Resources. If none of the meetings with Human Resources are to be consecutive, how many different ways can he arrange the five meetings?

A) 12
B) 15
C) 13
D) 6
E) 36

Source: Math Bible (Jeff Sacksmann)

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Originally posted by DarkHorse2019 on 03 Aug 2019, 01:06.
Last edited by DarkHorse2019 on 05 Aug 2019, 06:53, edited 1 time in total.
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Re: An executive is planning his morning schedule,which will include five  [#permalink]

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New post 03 Aug 2019, 04:30
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Official Explanation

To avoid back-to-back HR meetings, the HR meetings must be 1st,
3rd, and 5th. Thus, the 1st meeting could be any of the 3 HR meetings, the 2nd
could be either of the 2 other meetings, the 3rd could be either of the remaining
HR meetings, while the 4th is the remaining other meeting and the 5th is the
remaining HR meeting. The number of permutations is:
3 x 2 x 2 x 1 x 1 = 12

1st HR _____ 2nd HR _____ 3rd HR
3 2 2 1 1
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Re: An executive is planning his morning schedule,which will include five  [#permalink]

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New post 03 Aug 2019, 07:17
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DarkHorse2019 wrote:
An executive is planning his morning schedule, which will include
five meetings, three of which are with Human Resources. If none
of the meetings with Human Resources are to be consecutive,
how many different ways can he arrange the five meetings?

A) 12
B) 15
C) 13
D) 6
E) 36

Source: Math Bible (Jeff Sacksmann)


Given: An executive is planning his morning schedule, which will include five meetings, three of which are with Human Resources. None of the meetings with Human Resources are to be consecutive,
Asked: How many different ways can he arrange the five meetings?

Three meetings with HR are to be conducted at 1st, 3rd and 5th place (3! ways) and other meeting are to be conducted at 2nd and 4th place.(2! ways)
Total number of ways for 5 meetings = 3!*2! = 6*2 = 12

IMO A
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Re: An executive is planning his morning schedule,which will include five  [#permalink]

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New post 03 Aug 2019, 07:43
1
Hi, can any one help me in this..

Can this be done with first taking the possible number of meetings in 5 ways and then subtracting the 3 HR meetings together. Represented as 5!- 5P3.

I dint get the answer right, please can someone tell me where did I go wrong???

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Re: An executive is planning his morning schedule,which will include five  [#permalink]

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New post 05 Aug 2019, 04:25
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Shef08 wrote:
Hi, can any one help me in this..

Can this be done with first taking the possible number of meetings in 5 ways and then subtracting the 3 HR meetings together. Represented as 5!- 5P3.

I dint get the answer right, please can someone tell me where did I go wrong???

Posted from my mobile device



Hi Shef08,

You have subtracted all cases where {HR}{HR}{HR} come together but in this case you have to subtract where two {HR}{HR} come together also. Even two HR meetings back to back are not allowed. Hence we have to subtract all cases where we have {HR}{HR}{HR} and also cases where we have {HR}{HR}.
Going by this way will be very tedious. Hence better to do it {HR}P{HR}P{HR} this way where P is non HR meeting.
3*2*2*1*1 = 12
Hope this helps !
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Re: An executive is planning his morning schedule,which will include five  [#permalink]

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New post 05 Aug 2019, 07:26
stne wrote:
Shef08 wrote:
Hi, can any one help me in this..

Can this be done with first taking the possible number of meetings in 5 ways and then subtracting the 3 HR meetings together. Represented as 5!- 5P3.

I dint get the answer right, please can someone tell me where did I go wrong???

Posted from my mobile device



Hi Shef08,

You have subtracted all cases where {HR}{HR}{HR} come together but in this case you have to subtract where two {HR}{HR} come together also. Even two HR meetings back to back are not allowed. Hence we have to subtract all cases where we have {HR}{HR}{HR} and also cases where we have {HR}{HR}.
Going by this way will be very tedious. Hence better to do it {HR}P{HR}P{HR} this way where P is non HR meeting.
3*2*2*1*1 = 12
Hope this helps !




Awesome!!! Loved your simple explanation to this
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Re: An executive is planning his morning schedule,which will include five   [#permalink] 05 Aug 2019, 07:26
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