I don't understand what I am doing wrong for this question "In how many ways can a President, Vice-President, and Treasurer be chosen from a group of  4 guys and 4 girls and at least one girl and at least one guy holds at least one of those three positions? One person cannot serve in more than one position."

I tried doing 4*4*6 (for 4 boys and 4 girls then 6 for the remaining people). Could I get some help? Thanks :)

 Aug 7, 2020

My GUESS  (often wrong with these Q's)


4 c 1   for a girl in one of the offices    = 4 ways

    times    4c1  for a boy                      = 16 ways

       can be    bgx     bxg   xbg     gbx   gxb   xgb        6 x 16 = 96 

      one office left   choose from 6 remaining          96 x 6 = 576      ways     (?????)



 Let me know if I am incorrect...... and what the REAL answer is !   THANX !    ~EP

 Aug 7, 2020

Hi EP! I tried doing this problem, and I got a different answer from you...but nice job! (you might actually be the right one!)


Here is how I did it:

Since there are a total of 8 people, we start out by multiplying by 8.

Next, whether the person is a boy or a girl, we need to choose someone from the other gender. That gives us 4.

Now, we multiply by what is remaining, which is 6.

8*4*6 = 192


I'm not to good with these questions either (my brain just keeps on thinking about "what ifs"), so my answer might not be correct.



ilorty  Aug 7, 2020

37 Online Users