Given:

Total number of questions = 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 ways of answering 5 questions from part A and 5 questions from part B) + (No. of ways of answering 6 questions from part A and 4 from part B)

= (^{6}C_{4} × ^{7}C_{6}) + (^{6}C_{5} × ^{7}C_{5}) + (^{6}C_{6} × ^{7}C_{4})

By using the formula,

^{n}C_{r} = \( \dfrac{ n!}{r!(n – r)!}\)

= (15×7) + (6×21) + (1×35)

= 105 + 126 + 35

= 266

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

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