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Question

There are 3 sections in a question paper each containing 5 questions. A candidates has to solve only 5 questions, choosing at least one question from each section. In how many ways can he make his choice?

A
15C5
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B
3C1×12C4
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C
2250
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D
None of these
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Solution

The correct option is A 2250
Let there are 3 section namely a,b,c. Each having 5 question. A candidate has to solve only 5 question. Candidate can choose 'one' que. from section 'a', 'one' question from section 'b' & 'three' question from section 'c' Which can be choosen in5c15c15c3 ways. Again, 'one' que from section 'a', 'three' ques from section 'b', & 'one' ques section 'c'. Which can be choosen in 5c15c35c1 ways Again, 'three'question from section 'a', 'one'que from section 'b', & 'one' que from section 'c' Which can be choosen in5c35c15c1 Candidate can also choose 'two' que from section 'a', 'two' que from section'b', & 'one' que from section 'c' Which can be choosen in5c25c25c1 ways Again, 'two'que from section 'a', 'two' que from section'b', & 'one'que from section 'c'. Which can be choosen in5c25c25c1 ways Again, 'one'que from section 'a', 'two' que from section 'b',& 'two' que from section'c' Which can be choosen in- 5c15c25c2 Total no. Of ways to choose 5 questions - (5c15c15c3)3 + (5c15c25c2) = 2250

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