Team assignments with two people barred from research

Question

Ten staff must be split into three teams: $3$ quant researchers, $4$ quant traders and the remaining $3$ as quant developers. Two of the staff cannot do research and must not be put on the research team. In how many ways can the teams be formed?

Short answer

$1960$ . Pick the research team from the $8$ eligible people, $\binom83=56$ ways, then pick the traders from the $7$ who remain, $\binom74=35$ ways; the developers are whoever is left. $56\cdot35=1960$ .

Adapted from OpenQuant; question and answer rewritten by SelfMadeQuant.com.

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Lessons behind this question

Counting and Combinatorics

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