A committee of two students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?  Options:
A) 3	B) 4	C) 5	D) 6	E) 8
Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?   Your approach: total 10 options, 5c3.   Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.   This gives us   10-3-3= 
<gadget id="calculator">  10-3-3</gadget>
<output>4</output>
4 as the answer.   Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, 4DE   4
<result>B</result>
A committee of two students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?