How many ways can you choose a project management team consisting of a project manager, a systems analyst and three programmers if there are two project managers, 4 systems analysts and 6 programmers to choose from?

In probability problems like this one, the combination and fundamental counting principles are applied. The fundamental counting principle follows that if the are 'a' ways of choosing object 1, and 'b; way of choosing object 2, the total ways would be a*b. The combination problem is when 'n' objects are taken 'r' at a time, or written conveniently as nCr. Combining these two would be:

Project Manager x System Analyst x Programmers
2C1 x 4C1 x 6C3 = 160 ways

Note: nCr can be solved easily using the scientific calculator using the nCr button. But basically nCr can be manually solved using the formula 

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