A president and treasurer are to be chosen from a student club consisting of 50 members. How many different choices of officers are possible if B and C will serve together or not at all?

Question

kropot72 · Answer

If B and C are excluded there are P(48, 2) permutations of the remaining members. In addition there are 2 permuations of B and C in the positions of president and treasurer. Therefore the total number of choices is given by:
$$\large P(48, 2)+2=(48\times47)+2=you\ can\ calculate$$

anonymous · Answer

Thanks A lot. Another Question,  How many choices if A and B will not serve together? 
should i write P(49,2) + P(49,2) or P(50,2) - P(2,2) ?

kropot72 · Answer

If we assume that the condition "B and C will serve together or not at all" no longer applies, the question can be approached as follows:
If A and B had agreed to serve together, there would have been two permutations of their joint service among the total number of permutations of the 50 students taken two at a time. Therefore if A and B will not serve together, the total number of choices is given by P(50, 2) - P(2, 2).

anonymous · Answer

Thank you a lot!

kropot72 · Answer

You're welcome :)