[tex]C_{3x+7}^{6x+2} \\ \\ 3x+7 \geq 6x+2 \Rightarrow x \leq \dfrac{5}{3} \\ \\ 3x+7\geq 0,\quad 6x+2 \geq 0 \Rightarrow x \geq -\dfrac{1}{3} \\ \\ x \in \Big[-\dfrac{1}{3},\dfrac{5}{3}\Big] \\ \\ \text{Stim ca cea mai mare combinare este elementul din mijloc al}\\ \text{sirului binomial.}\\ \\ x =\dfrac{-\dfrac{1}{3}+\dfrac{5}{3}}{2} = \dfrac{2}{3} \\ \\ \Rightarrow \max\Big(C_{3x+7}^{6x+2}\Big) = C_{3\cdot \frac{2}{3}+7}^{6\cdot \frac{2}{3}+2} = C_{9}^6 = 84[/tex]
=> b) M = 84
