BN1989 wrote:
A committee of 3 people is to be chosen from the president and vice president of four different companies. What is the number of different committees that can be chosen if two people who work for the same company cannot both serve on the committee?
A) 16
B) 24
C) 28
D) 32
E) 40
Now this is quite amusing, i would consider the P & VP to be a couple
So there will be 4 couples, out which we need a committee which wont have one
Total number of ways, without any restriction =\(5C_3\) = 56 ways
Now if we keep a restriction we can calculate the ways in which one couple is present = \(4C_1 * 6C_1\)= 24 ways
Now the difference will give us 32 ways
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If you notice any discrepancy in my reasoning, please let me know. Lets improve together.
Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.