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Bunuel
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if Dave should get either three paintings or five paintings? (All paintings should be given away).

A) 120
B) 252
C) 372
D) 1092
E) 2100

Veritas Prep Official Solution



There are two ways of distributing the paintings in this case:

Dave gets 3 paintings and Mona gets the rest: You select 3 of the 10 paintings and give them to Dave. This can be done in 10C3 = 120 ways

Dave gets 5 paintings and Mona gets the rest: You select 5 of the 10 paintings and give them to Dave. This can be done in 10C5 = 252 ways

Total number of ways in which you can distribute the paintings = 120 + 252 = 372 ways
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Hi, just a small question.
Why have we not calculated anything for Mona and just calculated the total possible ways for Dave as our final answer?
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Bunuel
In how many ways can 10 different paintings be distributed between two collectors – Dave and Mona – if Dave should get either three paintings or five paintings? (All paintings should be given away).

A) 120
B) 252
C) 372
D) 1092
E) 2100


If Dave gets 5 paintings, the number of ways that can happen is:

10C5 = (10 x 9 x 8 x 7 x 6)/(5 x 4 x 3 x 2) = 3 x 2 x 7 x 6 = 252 ways

If Dave gets 3 paintings the number of ways that can happen is:

10C3 = (10 x 9 x 8)/(3 x 2) = 5 x 3 x 8 = 120 ways

So, the total 252 + 120 = 372 ways.

Answer: C
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