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?  Choose the correct option:
A) 16
B) 24
C) 28
D) 32
E) 40
i just did the total number of possibilities first:   ab cd ef gh are the 4 companies for example   8c3. this will include the problem counts of a pres/vp of the same company   how many ways did we over count = How many ways can a president and VP of the same company be part of this group?   choose the group, 4c1, then take both the president and vp, 2c2, then a remaining member from one of the other 3, 6c1   4c1 * 2c2 * 6c1   4 * 1 * 6= 
<gadget id="calculator">4 * 1 * 6</gadget>
<output>24</output>
24   8c3 - 24= 56 - 24= 
<gadget id="calculator">56 - 24</gadget>
<output>32</output>
32 answer is 32
<result>D</result>
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?