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A student is asked to answer 10 out of 13 questions is an examination such that he must answer atleast four questions from the first five questions. The number of choices available to him is
Options:
Solution:
2325 Upvotes
Verified Answer
The correct answer is:
196
Case I
4 questions from first 5 questions and 6 questions from remaining 8 questions
$$
\therefore \quad{ }^5 C_4 \times{ }^8 C_6=5 \times 28=140
$$
Case II
Choose 5 questions from first 5 questions and next 5 questions from remaining 8 questions
$$
\because \quad{ }^5 C_5 \times{ }^8 C_5=1 \times 56=56
$$
Total number $=140+56=196$
4 questions from first 5 questions and 6 questions from remaining 8 questions
$$
\therefore \quad{ }^5 C_4 \times{ }^8 C_6=5 \times 28=140
$$
Case II
Choose 5 questions from first 5 questions and next 5 questions from remaining 8 questions
$$
\because \quad{ }^5 C_5 \times{ }^8 C_5=1 \times 56=56
$$
Total number $=140+56=196$
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