Question

Answer this
Hint: Permutation and Combination​

Answer 1

I hope it can helps you...

Answer 2

$\large \textit{According to\ \ \ ^n\!C_r\ = \ ^n\!C_{n-r} } \\ \\ \\ ^{18}C_r \ = \ ^{18}C_{18-r} \ = \ ^{18}C_{r+2} \\ \\ \\ 18-r=r+2 \\ \\ r+r=18-2 \\ \\ 2r=16 \\ \\ r=8$

$\Large \textit{Now let's find \ ^r\!C_5 . }$

$\displaystyle ^r\!C_5 \ = \ ^8\!C_5 \ = \ \frac{8!}{5! \times 3!} \ = \ \frac{8 \times 7 \times 6 \times 5!}{5! \times 6} \ = \ 8 \times 7 \ = \ \bold{56}$

$\LARGE \textbf{Thus the answer is 56.}$