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# Seven different objects must be divided among three people. In how man

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Senior Manager
Joined: 12 Jan 2019
Posts: 263
Seven different objects must be divided among three people. In how man  [#permalink]

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12 Jan 2019, 23:30
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Seven different objects must be divided among three people. In how many ways can this be done
if at least one of them gets exactly 1 object?
(a) 2484
(b) 1218
(c) 729
(d) 625
(e) None of these

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Senior Manager
Joined: 12 Jan 2019
Posts: 263
Re: Seven different objects must be divided among three people. In how man  [#permalink]

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12 Jan 2019, 23:32
If only one gets 1 object
The remaining can be distributed as: (6,0) , (4, 2), (3, 3).
(7C1 × 6C6 × 3! + 7C1 × 6C4 × 3! + 7C1 × 6C3 × 3!/2!)
= 42 + 630 + 420 + 1092.
If 2 people get 1 object each:
7C1 × 6C1 × 5C5 × 3!/2! = 126.
Thus, a total of 1218.
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Re: Seven different objects must be divided among three people. In how man   [#permalink] 12 Jan 2019, 23:32
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