Question

Find n if n + 1C6: nC5 = 11: 6.​

Answer 1

$n = 10$

Step-by-step explanation:

$Given, \\ n + 1C_{6} : nC_{5} = 11 : 6 \\ \frac{(n + 1) !}{6 ! \times (n + 1 - 6)!} \div \frac{n !}{5! \times (n - 5)!} = \frac{11}{6} \\ \frac{(n + 1) !}{6 ! \times (n - 5)!} \times \frac{5! \times (n - 5)!}{n!} = \frac{11}{6} \\ \frac{(n + 1) \times n !}{6 \times 5! \times (n - 5)!} \times \frac{5! \times (n - 5)!}{n!} = \frac{11}{6} \\ \frac{n + 1}{6} = \frac{11}{6} \\ n + 1 = 11 \\ n = 10$