Answer 1

Given:
 ²⁴C_x = ²⁴C_{2x + 3}
We have,

\[24 = x + 2x + 3\] [∵\[{}^n C_x = {}^n C_y \Rightarrow x = y\]]  or, \[n = x + y\]

\[\Rightarrow 24 = 3x + 3\]
\[ \Rightarrow 3x = 21\]
\[ \Rightarrow x = 7\]