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# GMAT Diagnostic Test Question 39

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GMAT Diagnostic Test Question 39 [#permalink]  07 Jun 2009, 00:03
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GMAT Diagnostic Test Question 39

Field: combinations
Difficulty: 650

Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252
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Last edited by Bunuel on 26 Nov 2013, 13:10, edited 5 times in total.
Updated.
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Re: GMAT Diagnostic Test Question 39 [#permalink]  26 Nov 2013, 13:04
Could you update the question on this page to match the question in the downloadable PDF(8 small, 2 large). It took me a while to figure out that the solutions on this page don't match the question at the top of the page(7 small books, 3 large).
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Kudos [?]: 47499 [1] , given: 7123

Re: GMAT Diagnostic Test Question 39 [#permalink]  26 Nov 2013, 13:12
1
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2
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UPDATED.

SOLUTION:
Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: $$C^5_8+C^4_8*C^1_2=56+140=196$$.

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GMAT 1: 490 Q32 V25
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Kudos [?]: 11 [0], given: 34

Re: GMAT Diagnostic Test Question 39 [#permalink]  16 Dec 2013, 03:24
Bunuel wrote:
UPDATED.

SOLUTION:
Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: $$C^5_8+C^4_8*C^1_2=56+140=196$$.

Dear Bunuel,
thanks a lot for your priceless help...
meanwhile could you give alternative way to solve with no formula? cause im just a beginner and it a bit hart to me to keep with formulas
thanks a lot
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Math Expert
Joined: 02 Sep 2009
Posts: 28782
Followers: 4594

Kudos [?]: 47499 [0], given: 7123

Re: GMAT Diagnostic Test Question 39 [#permalink]  16 Dec 2013, 06:43
Expert's post
3111987 wrote:
Bunuel wrote:
UPDATED.

SOLUTION:
Romi has a collection of 10 distinct books out of which 8 are small and 2 are large. In how many ways can he select 5 books to take with him on a trip if he can take at most 1 large book?

A. 56
B. 126
C. 152
D. 196
E. 252

Since Romi can take at most 1 large book then he can take with him either 5 small books or 4 small books and 1 large book: $$C^5_8+C^4_8*C^1_2=56+140=196$$.

Dear Bunuel,
thanks a lot for your priceless help...
meanwhile could you give alternative way to solve with no formula? cause im just a beginner and it a bit hart to me to keep with formulas
thanks a lot

$$C^5_8=\frac{8!}{(8-5)!5!}=56$$ is the number of ways we can choose 5 items out of 8.

Theory on Combinations: math-combinatorics-87345.html

DS questions on Combinations: search.php?search_id=tag&tag_id=31
PS questions on Combinations: search.php?search_id=tag&tag_id=52

Tough and tricky questions on Combinations: hardest-area-questions-probability-and-combinations-101361.html

Hope it helps.
_________________
Re: GMAT Diagnostic Test Question 39   [#permalink] 16 Dec 2013, 06:43
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# GMAT Diagnostic Test Question 39

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