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Bunuel
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: \(C^5_8+C^4_8*C^1_2=56+140=196\).

Answer: D.


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 :( :oops:
thanks a lot :wink:
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Bunuel
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: \(C^5_8+C^4_8*C^1_2=56+140=196\).

Answer: D.


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 :( :oops:
thanks a lot :wink:

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

Check below links for more:
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.

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