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