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From ten people, how many ways can you form a team of eight people consisting of a project manager, two (equivalent) deputy project managers, and five (equivalent) engineers?

Aug 14, 2021

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There are 10 ways to pick a project manager

$$\binom{9}{2} = \frac{9 \times 8}{2 \times 1} = 36$$ ways to pick two deputy project managers

$$\binom{7}{5} = \binom{7}{2} = \frac{7 \times 6}{2 \times 1} = 21$$ways to pick five engineers

$$10 \times 36 \times 21 = \boxed{7560}$$

Aug 14, 2021