SOLUTION: A group of 4 teachers,9 truckers, and 11 lawyers are going to form a committee of 2. How many different ways can the committee be formed with people from different professions?

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Question 629155: A group of 4 teachers,9 truckers, and 11 lawyers are going to form a committee of 2. How many different ways can the committee be formed with people from different professions?
Answer by Edwin McCravy(20054) About Me  (Show Source):
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A group of 4 teachers,9 truckers, and 11 lawyers are going to form a committee of 2. How many different ways can the committee be formed with people from different professions?
We must break this into three cases:

1.  A teacher and a trucker

4 ways to choose the teacher times 9 ways to 
choose the trucker = 4×9 = 36 ways.

2.  A teacher and a lawyer

4 ways to choose the teacher times 11 ways to 
choose the lawyer = 4×11 = 44 ways.

3.  A trucker and a lawyer

9 ways to choose the trucker times 11 ways to 
choose the lawyer = 9×11 = 99 ways.

Total number of ways:  36 + 44 + 99 = 179 ways.

Edwin