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

Question

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.

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

iamdp · Answer

hi

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

chetan2u · Answer

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...

iamdp · Answer

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

chetan2u · Answer

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...
your answer 6720(including ways where each set order has been taken separate..) so answer =6720/3!=6720/6=1120
hope it helped

ak1802 · Answer

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.

Multiply 56 by 20 and your answer is 1120.

D.

Posted from my mobile device

sterling19 · Answer

"...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.

iamdp · Answer

Hi thanks for your reply I get it now

masoomdon · Answer

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)

Bunuel · Answer

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)

GMATGuruNY · Answer

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

D

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards