A firm employs 10 programmers 8 systems analysts 4 computer

A firm employs 10 programmers, 8 systems analysts, 4 computer engineers, and 3 statisticians. A \"team\" is to be chosen to handle a new long term project. The team will consist of 3 programmers, 2 systems analysts, 2 computer engineers, and 1 statistician.

a) In how many ways can the team be chosen? explain

b) If the customer insists that one particular engineer with whom he or she has worked before be assigned to the project, in how many ways can the team be chosen? Explain

Solution

a)

There are 10C3 ways to choose 3 programmers.

There are 8C2 ways to choose 2 system analysts.

There are 4C2 ways to choose computer engineers.

There are 3C1 ways to choose a statistician.

Hence, there are

(10C3)(8C2)(4C2)(3C1) = 60480 ways [ANSWER]

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b)

In that case, there are only 3C1 ways to choose the other computer engineer. Hence,

(10C3)(8C2)(3C1)(3C1) = 30240 ways [ANSWER]