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M37-20

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Bunuel
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M37-20 [#permalink] New post   19 Nov 2021, 09:53
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65% (hard)

Question Stats:

44% (01:47) correct 56% (01:14) wrong based on 16 sessions
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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. \(3,600\)
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C
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Bunuel
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Re M37-20 [#permalink] New post   19 Nov 2021, 09:53
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Official Solution:

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
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Re: M37-20 [#permalink] New post   01 May 2024, 16:27
Question stem says ron and hermione refuse to go together. Answer stem includes ron and hermione going together. Please revise question/answer thank you.
Bunuel wrote:
Official Solution:

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

­
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Re: M37-20 [#permalink] New post   02 May 2024, 00:05
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unicornilove wrote:
Question stem says ron and hermione refuse to go together. Answer stem includes ron and hermione going together. Please revise question/answer thank you.
Bunuel wrote:
Official Solution:

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

­

It seems you did not read the solution carefully. The question indeed asks to find the number of groups without Ron and Hermione together. We find this by subtracting the number of groups with them (restriction condition) from the total number of groups, thus getting the number of groups without them. This is clearly given in the solution: "Total - Restriction = 2^7 - 2^5 = 2^5(2^2-1) = 96".
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Re: M37-20 [#permalink]
02 May 2024, 00:05
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