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A tech startup is distributing 4 new laptops among 3 project teams. Ev
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04 Aug 2026, 00:26
04 Aug 2026, 00:26
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Question Stats:
75% (01:23) correct
25% (01:54) wrong based on 4 sessions
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A tech startup is distributing 4 new laptops among 3 project teams. Every team must receive at least one laptop, and any team may receive more than one. In how many different ways can the laptops be distributed so that no team is left without one?
(A) 24
(B) 33
(C) 36
(D) 64
(E) 81
(A) 24
(B) 33
(C) 36
(D) 64
(E) 81
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Re: A tech startup is distributing 4 new laptops among 3 project teams. Ev
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06 Aug 2026, 13:19
06 Aug 2026, 13:19
Expert Reply
Explanation
Assume the 4 laptops are different (Laptop 1, 2, 3, 4) and the 3 project teams are different.
First count all the possible distributions
Each laptop can go to any of the 3 teams:
\(3^4=81\)
Now, remove cases where a team gets no laptop
If one specific team is empty, the 4 laptops can only go to the other 2 teams:
\(2^4=16\)
There are 3 choices for which team is empty:
\(3(16)=48\)
Add back cases where two teams are empty
If two teams are empty, all laptops go to the remaining one team: 3 ways
(Each of the 3 teams could be the only team receiving laptops.)
\(81−48+3=36\)
Therefore: 36
Answer: (C)
Assume the 4 laptops are different (Laptop 1, 2, 3, 4) and the 3 project teams are different.
First count all the possible distributions
Each laptop can go to any of the 3 teams:
\(3^4=81\)
Now, remove cases where a team gets no laptop
If one specific team is empty, the 4 laptops can only go to the other 2 teams:
\(2^4=16\)
There are 3 choices for which team is empty:
\(3(16)=48\)
Add back cases where two teams are empty
If two teams are empty, all laptops go to the remaining one team: 3 ways
(Each of the 3 teams could be the only team receiving laptops.)
\(81−48+3=36\)
Therefore: 36
Answer: (C)
gmatclubot
Re: A tech startup is distributing 4 new laptops among 3 project teams. Ev [#permalink]
06 Aug 2026, 13:19
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