TalonShade
I am trying to do this using the counting method and would appreciate some help where I'm going wrong. I got the correct answer using formulas but cant seem to with the counting method.
So basically
Total ways of selecting 4 of 7 will give us all the ways - 7x6x5x4
And subtracting the following should give us the desired answer
1. Where Ben is a semifinalist but Ann is not - 1 x 5 x 4 x 3 ----- (a)
2. Where Ann is a semifinalist but Ben is not - 1 x 5 x 4 x 3 ----- (b)
T -(a+b) = 840 -(60+60) = 740 --- ???
It is selection and you are taking arrangements.
So T = 7C4 = 35
a) B is one, so choose remaining 3 from available 5( less A and B) = 5C3 = 10
b) A and n(B): Similarly 10 ways for A being a part and B not being a part.
c) both (A and B): Also add ways where both A and B are part, so choose 2 out of remaining 5 = 5C2 = 10
Our answer = 35-10-10-10 = 5
A
There are various combinations in which above 3 could be calculated.
It could be (T-(A as one)-(B there but not A))=35-6C3-5C3=35-20-10=5
OR T-(A)-(B)+both(A and B)=35-20-20+10=5