量化人员分组

在这个限制下，我们只需关注那两名不能进入研究组的员工。把他们被分到不同团队的情况数与被分到同一团队的情况数相加，就能得到满足条件的总分组数。

如果他们被分到不同团队，那么一人会去量化交易组，另一人会去量化开发组。对于交易组，我们先从这两名不能做研究的员工中选 1 人，再从另外 8 名员工中选 3 人补足交易组。对于开发组，剩下那 1 名受限员工必须进入开发组，再从其余 5 名员工中选 2 人。剩下的人进入研究组。于是有： $$\begin{equation*} {2\choose1}{8\choose3}\cdot{1\choose1}{5\choose2} \cdot {3\choose3} = 1120 \end{equation*}$$

如果这两名员工被分到同一团队，那么他们只能一起进入量化交易组或量化开发组。若他们都在交易组，则先选中这两人，再从另外 8 名不受限制的员工中选 2 人进入交易组。随后开发组从剩下的 6 名不受限制员工中选 3 人，其余进入研究组。用同样的思路，也可以数出两名不擅长研究的员工同时进入量化开发组的情况数，因此他们同组时的总数为：

$$\begin{equation*} {2\choose2}{8\choose2}\cdot{6\choose3}\cdot {3\choose3} + {2\choose2}{8\choose1}\cdot{7\choose4}\cdot {3\choose3} = 840 \end{equation*}$$

团队分配总数就是这两类情况之和，因此最终答案为： $$\begin{equation*} 1120 + 840 = \boxed{1960} \end{equation*}$$

---

Original Explanation

Given these conditions, we should only focus on the two employees that have restrictions to which team they can work on. Summing the number of ways they can work on different teams with the number of ways they can work on the same team will give us the total number of combinations that fulfill the requirement.

If they work in different teams, one will be in quant trading and the other will be in quant development. For trading, we have two of the inexperienced research members to select from, and then eight of the other employees to select the remaining traders from. For quant development we have just one experienced member left to select and five of the other employees from which we choose two. The remaining go to quant research. This gives us: $$\begin{equation*} {2\choose1}{8\choose3}\cdot{1\choose1}{5\choose2} \cdot {3\choose3} = 1120 \end{equation*}$$

If the inexperienced members work on the same team, they can either work together on the quant trading team or quant developer team. If it's the trading team, we select both of the members and two of the eight non-restricted members to be on the trading team. The development team will then get three of the six remaining non restricted members. Rest will go to research. Using similar logic we can count the number of ways we can form teams such that the two research inexperienced members are both on the quant development team, making our total for when they are on the same team:

$$\begin{equation*} {2\choose2}{8\choose2}\cdot{6\choose3}\cdot {3\choose3} + {2\choose2}{8\choose1}\cdot{7\choose4}\cdot {3\choose3} = 840 \end{equation*}$$

The total number of teams arrangments that can be formed is the union of these giving us a final answer of: $$\begin{equation*} 1120 + 840 = \boxed{1960} \end{equation*}$$