PTRIV
Hi, I came across this question in the quiz yesterday . Can anyone provide a good explanation :
Harry is planning a journey to Hogwarts. He can go alone or with any number of his 7 friends: Ron, Hermione, Hagrid, Luna, Neville, Fred and George. If Ron and Hermione refuse to go together, how many groups are possible for the journey ?
Harry is planning a journey to Hogwarts. He can go alone or with any number of his 7 friends: Ron, Hermione, Hagrid, Luna, Neville, Fred and George. If Ron and Hermione refuse to go together, how many groups are possible for the journey ? A. \(88\)
B. \(95\)
C. \(96\)
D. \(1,560\)
E. \(3,600\)
How many groups are possible if we did not have the restriction? Without the restriction the total number of groups possible is \(2^7\): each of Harry's 7 friends can either join Harry or not.
How many groups are possible with Ron and Hermione in them? If Ron and Hermione are in the group, then each of the 5 remaining friends can either join or not, so the number of groups with Ron and Hermione is \(2^5\).
So, there are \(Total-Restriction=2^7-2^5=2^5(2^2-1)=96\) groups possible.
Answer: C
Discussed here:
https://gmatclub.com/forum/harry-is-pla ... 65289.htmlHope it helps.