In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

Question

Filo · Accepted Answer

Solution: selection for I & II
when 3,5 selected

.^{5} C_{3} .^{7} C_{5}

when 4, 4 selected

.^{5} C_{4} .^{7} C_{4}

when 5,3 slected

.^{5} C_{5} .^{7} C_{3}

required =

\frac{5 !}{3 ! 2 !} \cdot \frac{7 !}{5 ! 2 !} + \frac{5 !}{4 ! 1 !} \cdot \frac{7 !}{4 ! 3 !} + \frac{5 !}{5 ! 0 !} \cdot \frac{7 !}{3 ! 4 !}

=

7 \cdot 6 \cdot 5 + 5 \cdot 7 \cdot 5 + 7 \cdot 5

= 210 + 175 + 35

= 210 + 210 = 420

answer

Question Text	In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?
Answer Type	Text solution:1
Upvotes	150

In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

Text solutionVerified

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