Problem Solving

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

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.

Hi,
I think the same.
And I'll go with 127
different ways we can handle this:
1L + 4S--------------->3*(choosing 4 element of a set of 7 elements) =3*35=105
2L+S------------------>3*7=21 state
7S-------------------->1 state
total=21+1+105=127

Is it correct?

sorry I saw the reply a second later

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
3 large
and 1 large = 3 small
Total space available -- 1 large and 4 small books

Case 1--- 1 large and 4 small
3*7C4 = 3*35 = 105

case 2--- 2 large and 1 small
3C2*7 = 3*7 = 21

Case 3- 7 small books
1 way

Total 126+1 =127