Answer:
36
Step-by-step explanation:
We have been given that you have 8 friends, of whom 5 will be invited to your big party in IV on Friday night. We are asked to find the number of choices if 2 of the friends are feuding and will not attend together.
We can choose 5 friends from 8 friends in [tex]^8C_5[/tex] ways.
[tex]^8C_5=\frac{8!}{5!(8-5)!}=\frac{8!}{5!(3)!}=\frac{8*7*6*5!}{5!*3*2*1}=8*7=56[/tex]
Therefore, we can choose 5 friends from 8 friends in 56 ways.
Since two friends are feuding, so we need to choose 3 friends from 6 friends and subtract them from total ways.
We can choose 3 friends from 6 friends in [tex]^6C_3[/tex] ways.
[tex]^6C_3=\frac{6!}{3!(6-3)!}=\frac{6!}{3!(3)!}=\frac{6*5*4*3!}{3!*3*2*1}=5*4=20[/tex]
[tex]56-20=36[/tex]
Therefore, we have 36 choices, if 2 of the friends are feuding and will not attend together.
