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# Employees at a company will vote for an executive team of five people

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Math Expert
Joined: 02 Sep 2009
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Employees at a company will vote for an executive team of five people  [#permalink]

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10 Mar 2015, 06:08
2
5
00:00

Difficulty:

55% (hard)

Question Stats:

59% (02:02) correct 41% (02:01) wrong based on 147 sessions

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Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates?

A. 56
B. 120
C. 210
D. 1120
E. 6720

Kudos for a correct solution.

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Re: Employees at a company will vote for an executive team of five people  [#permalink]

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10 Mar 2015, 06:45
hi

Here first we'll select 5 out of 8 ie 8C5
now arrange it at 5 different positions [8C5] * 5! = 6720
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Re: Employees at a company will vote for an executive team of five people  [#permalink]

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10 Mar 2015, 07:01
1
1
iaak wrote:
hi

Here first we'll select 5 out of 8 ie 8C5
now arrange it at 5 different positions [8C5] * 5! = 6720

hi iaak,

you are missing out on one important point..
If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways= 8*7*20=1120..
ans D...
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Re: Employees at a company will vote for an executive team of five people  [#permalink]

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10 Mar 2015, 07:08
chetan2u wrote:
iaak wrote:
hi

Here first we'll select 5 out of 8 ie 8C5
now arrange it at 5 different positions [8C5] * 5! = 6720

hi iaak,

you are missing out on one important point..
If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways= 8*7*20=1120..
ans D...

Probably you are right my friend P & C is where am not good

Plz elaborate
question says that each team will be considered different as one person can hold multiple positions.
Can one guy be in all 5 positions.
i am not able to understand
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Re: Employees at a company will vote for an executive team of five people  [#permalink]

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10 Mar 2015, 07:19
iaak wrote:

Probably you are right my friend P & C is where am not good

Plz elaborate
question says that each team will be considered different as one person can hold multiple positions.
Can one guy be in all 5 positions.
i am not able to understand

hi ,
ill try to explain it to you..
th important point is..
If an executive team is considered different if any of the same people hold different offices
say 8 person are aA,B,C,D,E,F,G,H...
Let one way be
president is A..
treasurer is B..
members.. C,D,E.... now if members become D,C,E these will be same.. and it will change if one goes out say C,D,F...
this is the reason we divide the answer you have got by 3!.. as these 3 people can be placed in 3! amongst themselves...
hope it helped
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Employees at a company will vote for an executive team of five people  [#permalink]

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11 Mar 2015, 15:10
2
It's best to look at this question one part at a time.

8 total employees 5 potential executives. = 8!/5!3! = 56

Those 5 executives are made up of P, T, W,W,W. Use an anagram grid here to determine the total here. = 5!/3! = 20.

D.

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Employees at a company will vote for an executive team of five people  [#permalink]

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11 Mar 2015, 18:33
dpo28 wrote:
Plz elaborate
question says that each team will be considered different as one person can hold multiple positions.
Can one guy be in all 5 positions.

"...if any of the same people hold different positions" does not mean one person holds multiple positions. It means that the group is considered different only if the roles change.

You could be the first warrant officer selected in one group and the second warrant officer selected in the next group, but you are still a warrant officer either way. Your position has not changed, so the group is not "different" unless other people were moved around in the other roles. However, if you were president in one group and a warrant officer in a separate group, then the groups are considered different.

This is why we must divide by 3! to account for the combinations that just rotate the positions of the warrant officers but do not change the president or treasurer.
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Re: Employees at a company will vote for an executive team of five people  [#permalink]

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12 Mar 2015, 05:21
chetan2u wrote:
iaak wrote:

Probably you are right my friend P & C is where am not good

Plz elaborate
question says that each team will be considered different as one person can hold multiple positions.
Can one guy be in all 5 positions.
i am not able to understand

hi ,
ill try to explain it to you..
th important point is..
If an executive team is considered different if any of the same people hold different offices
say 8 person are aA,B,C,D,E,F,G,H...
Let one way be
president is A..
treasurer is B..
members.. C,D,E.... now if members become D,C,E these will be same.. and it will change if one goes out say C,D,F...
this is the reason we divide the answer you have got by 3!.. as these 3 people can be placed in 3! amongst themselves...
hope it helped

Hi
I get it now
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Joined: 07 Feb 2015
Posts: 45
Employees at a company will vote for an executive team of five people  [#permalink]

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Updated on: 15 Mar 2015, 21:47
2
Total number of candidates = 8
Total number of selections = 5
Number of ways to choose president=8
Number of ways to choose treasurer=7
considering all three warrant officer positions same, =6C3=20
Total way = 8x7x20=1120
(D)
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Originally posted by masoomdon on 12 Mar 2015, 05:56.
Last edited by masoomdon on 15 Mar 2015, 21:47, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 56251
Re: Employees at a company will vote for an executive team of five people  [#permalink]

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15 Mar 2015, 21:28
Bunuel wrote:
Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates?

A. 56
B. 120
C. 210
D. 1120
E. 6720

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:

We can use a quick formula for this. We have to go back to the Fundamental Counting Principle and think this through.

Choice #1: for the president, we have eight choices

Choice #2: for the treasurer, we have seven remaining choices

Choice #3: we have to pick 3 warrant officers from the remaining 6. This would be
6C3 = 20 choices.

The FCP tells us to multiply the number of choices in each selection:
8*7*20 = 56*20 = 1120 choices — Answer = (D)
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Re: Employees at a company will vote for an executive team of five people  [#permalink]

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18 Aug 2018, 14:02
Bunuel wrote:
Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams could be selected from the eight candidates?

A. 56
B. 120
C. 210
D. 1120
E. 6720

Number of options for president = 8. (Any of the 8 candidates.)
Number of options for treasurer = 7. (Any of the 7 remaining candidates.)
From the 6 remaining people, the number of ways to choose 3 to serve as warrant officers = 6C3 = (6*5*4)/(3*2*1) = 20.
To combine these options, we multiply:
8*7*20 = 1120

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Re: Employees at a company will vote for an executive team of five people   [#permalink] 18 Aug 2018, 14:02
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