Question

There are three sections A. B. C in a paper each section having 5 questions. In how many ways a student can solve exactly 5 questions taken at least one question from each section.

Answer 1

Answer:

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 in−5c 1 ∗5c 2 ∗5c 3 ways. Again, 'one' que from section 'a', 'three' ques from section 'b', & 'one' ques section 'c'. Which can be choosen in −5c

1∗5c 3∗5c 1 ways Again, 'three'question from section 'a', 'one'que from section 'b', & 'one' que from section 'c' Which can be choosen in−5c ∗5c 1 ∗5c 1

Candidate can also choose 'two' que from section 'a', 'two' que from section'b', & 'one' que from section 'c' Which can be choosen in−5c 2

∗5c 2∗5c 1 ways Again, 'two'que from section 'a', 'two' que from section'b', & 'one'que from section 'c'. Which can be choosen in−5c 1∗5c 2∗5c 1 ways Again, 'one'que from section 'a', 'two' que from section 'b',& 'two' que from section'c' Which can be choosen in- 5c 1 ∗5c 2 ∗5c 2 Total no. Of ways to choose 5 questions - (5c 2 ∗5c 1 ∗5c3 )∗3 + (5c1 ∗5c 2 ∗5c 2 ) = 2250

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Answer 2

$\blue{\huge{\underline{\underline{Answer:-}}}}$

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 in−5c1∗5c1∗5c3 ways. Again, 'one' que from section 'a', 'three' ques from section 'b', & 'one' ques section 'c'. Which can be choosen in −5c1∗5c3∗5c1 ways Again, 'three'question from section 'a', 'one'que from section 'b', & 'one' que from section 'c' Which can be choosen in−5c3∗5c1∗5c1  Candidate can also choose 'two' que from section 'a', 'two' que from section'b', & 'one' que from section 'c' Which can be choosen in−5c2∗5c2∗5c1 ways Again, 'two'que from section 'a', 'two' que from section'b', & 'one'que from section 'c'. Which can be choosen in−5c2∗5c2∗5c1 ways Again, 'one'que from section 'a', 'two' que from section 'b',& 'two' que from section'c' Which can be choosen in- 5c1∗5c2∗5c2  Total no. Of ways to choose 5 questions - (5c1∗5c1∗5c3)∗3 + (5c1∗5c2∗5c2) = 2250