A committee of four 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?
Choose the correct choice from the following answers:
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, BDE, CDE.   6
<result>D</result>
A committee of four 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?