baladon99 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?
A. 35
B. 56
C. 127
D. 196
E. 252
Source: GMATclub.com
If the question is re-phrased as the " how many ways can he arrange the books for his trip without wasting space" , will the answer remain the same ?
Thanks in advance
7 small books:
Number ways to choose 7 small books from 7 choices = 1.
1 large book, 4 small books:
Number of ways to choose 1 large book from 3 choices = 3.
Number of ways to choose 4 small books from 7 choices = 7C4 = 35.
To combine our options for each type of book, we multiply:
3*35 = 105.
2 large books, 1 small book:
Number of ways to choose 2 large books from 3 choices = 3C2 = 3.
Number of ways to choose 1 small book from 7 choices = 7.
To combine our options for each type of book, we multiply:
3*7 = 21.
Total number of ways to select the books = 1+105+21 = 127.
The correct answer is
C.
The number of ways to ARRANGE the books is MUCH higher. The GMAT would never ask for the number of arrangements; the solution is too involved for a GMAT question.
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