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

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Combination from A and from B ∷ \(\frac{4}{5};\frac{5}{5};\frac{6}{4}\)

Number of way to get \(\frac{4}{6}\) pattern = 6C4 × 7C6 

= \(\frac{6!}{2!\space4!}\times\frac{7!}{1!\space6!}\) 

= \(\frac{6.5}{2.1}\times\frac{7}{1}\) 

= 15 × 7 = 105 

Number of ways to get \(\frac{5}{5}\)pattern = 6C5 × 7C5 

= \(\frac{6!}{1!\space5!}\times\frac{7!}{2!\space5!}\) 

= \(\frac{6}{1}\times\frac{7\times6}{2\times1}\) 

= 6 × 21 = 126 

Number of ways to get the 6 4 pattern = 6C6 × 7C4 

= \(\frac{6!}{0!\space 6!}\times\frac{7!}{3!\space4!}\) 

= \(1\times\frac{7.6.5}{3.2.1}\)

= 35 

Hence, total number of ways= 105 + 126 + 35 

= 266

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