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Question -

A student has to answer 10 questions, choosing at least 4 from each of part A and part B. If there are 6 questions in part A and 7 in part B, in how many ways can the student choose 10 questions?



Answer -

Given:

Total number ofquestions = 10

Questions in part A =6

Questions in part B =7

Number of ways = (No.of ways of answering 4 questions from part A and 6 from part B) + (No. of waysof answering 5 questions from part A and 5 questions from part B) + (No. ofways of answering 6 questions from part A and 4 from part B)

= (6C4 × 7C6)+ (6C5 × 7C5) + (6C6 × 7C4)

By using the formula,

nCr = n!/r!(n – r)!

= (15×7) + (6×21) +(1×35)

= 105 + 126 + 35

= 266

∴ The total no. ofways of answering 10 questions is 266 ways.

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