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An examination paper consists of 12 questions divided into two

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An examination paper consists of $12$ questions divided into two parts $A$ & $B$ . Part $A$ , containing $7$ questions & part $B$ contains $5$ questions. A candidates is required to attempt $8$ questions selecting at least $3$ from each part. In how many ways can the candidates select the questions?

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Theodore Discussed

An examination paper consists of

12

questions divided into two parts

A

B

. Part

A

, containing

7

questions & part

B

contains

5

questions. A candidates is required to attempt

8

questions selecting at least

3

from each part. In how many ways can the candidates select the questions?

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Text solutionVerified

Student has to do

8

questions such that he does at least

3

questions from both the sets

How can he go about (Set I, Set II)

= (3, 5)

(4, 4)

(5, 3)

So, total number of ways of doing this is given by

5 C_{3} \times 7 C_{5}

5 C_{4} \times 7 C_{4}

5 C_{5} \times 7 C_{3}

= (10) (21) + (5) (35) + (1) (35) = 210 + 210 = 420

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Question Text	An examination paper consists of $12$ questions divided into two parts $A$ & $B$ . Part $A$ , containing $7$ questions & part $B$ contains $5$ questions. A candidates is required to attempt $8$ questions selecting at least $3$ from each part. In how many ways can the candidates select the questions?
Answer Type	Text solution:1
Upvotes	150