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A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
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The correct answer is:
196
196
As for given question two cases are possible.
(i) Selecting 4 out of first five question and 6 out of remaining 8 question $={ }^5 \mathrm{C}_4 \times{ }^8 \mathrm{C}_6=140$ choices.
(ii) Selecting 5 out of first five question and 5 out of remaining 8 questions $={ }^5 \mathrm{C}_5 \times{ }^8 \mathrm{C}_5=56$ choices.
Therefore, total number of choices $=140+56=196$.
(i) Selecting 4 out of first five question and 6 out of remaining 8 question $={ }^5 \mathrm{C}_4 \times{ }^8 \mathrm{C}_6=140$ choices.
(ii) Selecting 5 out of first five question and 5 out of remaining 8 questions $={ }^5 \mathrm{C}_5 \times{ }^8 \mathrm{C}_5=56$ choices.
Therefore, total number of choices $=140+56=196$.
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