Question 1083063: Board of directors of a company wants to
randomly form a quality management
committee of 5 members to monitor quality
of their products .
The company has 5
scientists , 4 engineers , and 6 accountants .
What is the probability that the committee
will contain 2 scientists , 1 engineer , and 2
accountants ?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! There are 5 scientists
There are 4 engineers
There are 6 accountants
In total there are 5+4+6 = 15 people.
Using the combination formula, there are 15 C 5 = 3003 ways to pick 5 people from a pool of 15 candidates. This is where order does not matter. With many committees, the members are equal in standing making order not important. That is the case here.
There are 5 C 2 = 10 different ways to pick 2 scientists from a pool of 5
There are 4 C 1 = 4 different ways to pick 1 engineer from a pool of 4
There are 6 C 2 = 15 different ways to pick 2 accountants from a pool of 6
Again order doesn't matter.
Multiply those results: 10*4*15 = 600
So there are 600 ways to pick 2 scientists, 1 engineer and 2 accountants
Divide the number of ways to get the outcome we want (600) over the total number of ways to pick a committee (3003) to get 600/3003 = 200/1001 = 0.1998 = 19.98%
The decimal and percent values are approximate
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Final Answer as a fraction: 200/1001
Final Answer as a decimal: 0.1998 (approximate)
Final Answer as a percentage: 19.98% (approximate)
These are all equivalent ways of stating the same thing. The answer you provide your teacher will depend on the instructions s/he gives you.
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