Restricted Team Formation

First count total assignments ignoring the restriction, then subtract or directly restrict who can fill Quant Research.

Choose the 3 Quant Researchers only from the 8 eligible employees.

1. 1. Choose Quant Researchers

   Since 2 employees are barred from Quant Research, choose all 3 researchers from the remaining 8: $\left(\genfrac{}{}{0ex}{}{8}{3}\right)=56$.

2. 2. Choose remaining teams

   From the remaining 7 employees, choose 4 for Quant Traders: $\left(\genfrac{}{}{0ex}{}{7}{4}\right)=35$; the last 3 automatically form Quant Developers.

3. 3. Multiply

   Total is $56\times 35=1960$.

   $$56\times 35=1960$$

Answer: 1960