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Romi has a collection of 10 different books that includes 7

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by varun289 » Sat Apr 13, 2013 10:52 am
Romi has a collection of 10 different books that includes 7 same size small and 3 same size large books. The size of 1 large book is equal to the size of 3 small books. In how many ways can he select books for his trip without wasting space, if he has space available for 1 large and 4 small books?

A. 35
B. 56
C. 127
D. 196
E. 252
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by Anju@Gurome » Sat Apr 13, 2013 11:28 am
varun289 wrote:Romi has a collection of 10 different books that includes 7 same size small and 3 same size large books. The size of 1 large book is equal to the size of 3 small books. In how many ways can he select books for his trip without wasting space, if he has space available for 1 large and 4 small books?
He should either select {1 large book and 4 small books} or {2 large books and 1 small book} or {4 + 3 = 7 small books}

Number of ways to select 1 large book and 4 small books = (3C1)*(7C4) = 3*35 = 105
Number of ways to select 2 large books and 1 small book = (3C2)*(7C1) = 3*7 = 21
Number of ways to select 7 small books = 1

Hence, total number of possible selections = (105 + 21 + 1) = 127

The correct answer is C.
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