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Question -

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups, each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. In how many ways can he choose the 7 questions?



Answer -

Given:

Total number ofquestions = 12

Total number ofquestions to be answered = 7

Number of ways = (No.of ways of answering 5 questions from group 1 and 2 from group 2) + (No. ofways of answering 4 questions from group 1 and 3 from group 2) + (No. of waysof answering 3 questions from group 1 and 4 from group 2) + (No. of ways ofanswering 2 questions from group 1 and 5 from group 2)

= (6C5 × 6C2)+ (6C4 × 6C3) + (6C3 × 6C4)+ (6C2 × 6C5)

By using the formula,

nCr = n!/r!(n – r)!

= (6×15) + (15×20) +(20×15) + (15×6)

= 90 + 300 + 300 + 90

= 780

∴ The total no. ofways of answering 7 questions is 780 ways.

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