The given equation is: \[ \binom{15}{8} + \binom{15}{7} = \binom{n}{r} \] We need to find the values of \(n\) and \(r\). \[\] Simplify the left-hand side We can apply Pascal's identity, which states: \[ \binom{n}{k} + \binom{n}{k+1} = \binom{n+1}{k+1} \] In our case, we have: \[ \binom{15}{8} + \binom{15}{7} = \binom{16}{8} \] [\]\ Express the equation Now, we have the equation: \[ \binom{16}{8} = \binom{n}{r} \] Determine \(n\) and \(r\) From this, we can conclude that: \[ n = 16, \quad r = 8 \] Thus, the values of \(n\) and \(r\) are: \[ n = 16, \quad r = 8 \]