Question

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?

Answer 1

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
`(n!)/(r!(n-r)!)`