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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
 #1
avatar+28021 
+2

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
 #2
avatar+1038 
+4

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

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