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After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?

Re: After a business trip to London, Michele has enough time to visit thre [#permalink]

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17 Jul 2016, 08:04

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Bunuel wrote:

After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?

A. 36 B. 48 C. 72 D. 96 E. 120

Number of ways of selecting 3 cities = 6C3=20. Lets say She decides to visit both Oslo and Stockholm and one other city, then number of ways of selecting the other city would be 4C1=4.

Thus, Number of ways of selecting three cities such that both Oslo and Stockhom are not chosen together = 20-4=16.

Since the question asks for the Sequence of the three cities, we will arrange the three cities to get all the possible outcomes.

Thus, Total different sequences will be 16 * 3! = 16*6 =96. Hence, the answer will be D.
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Re: After a business trip to London, Michele has enough time to visit thre [#permalink]

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17 Jul 2016, 08:06

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Bunuel wrote:

After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?

A. 36 B. 48 C. 72 D. 96 E. 120

Sequence of cities she can visit without any restrictions= 6*5*4= 120

Sequence of cities she can visit if she visits both Oslo and Stockholm on the same trip= 3*2 *1 *4 (after choosing Oslo and Stockholm, she is left with 4 cities to choose from)= 24

Sequence of cities to choose with restrictions= 120-24= 96

D is the answer
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Re: After a business trip to London, Michele has enough time to visit thre [#permalink]

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18 Jul 2016, 01:07

Hi Divyadisha,

Pls explain how did you arrive at the following sentence:

Sequence of cities she can visit if she visits both Oslo and Stockholm on the same trip= 3*2 *1 *4 (after choosing Oslo and Stockholm, she is left with 4 cities to choose from)= 24

Thanks, Pallavi

Divyadisha wrote:

Bunuel wrote:

After a business trip to London, Michele has enough time to visit three European cities before returning home. If she has narrowed her list to six cities that she'd like to visit - Paris, Barcelona, Rome, Munich, Oslo, and Stockholm - but does not want to visit both Oslo and Stockholm on the same trip, how many different sequences of three cities does she have to choose from?

A. 36 B. 48 C. 72 D. 96 E. 120

Sequence of cities she can visit without any restrictions= 6*5*4= 120

Sequence of cities she can visit if she visits both Oslo and Stockholm on the same trip= 3*2 *1 *4 (after choosing Oslo and Stockholm, she is left with 4 cities to choose from)= 24

Sequence of cities to choose with restrictions= 120-24= 96

I will be able to help you with my explanation for your comment.

The question asks for the number of sequences. Ex: Paris, Barcelona and Rome is one sequence. Paris, Rome and Barcelona is a different sequence. So the question tests you on permutations.

Without restriction, the first city to be visited can be chosen from any of the 6 given cities. The next city can be chosen from the remaining 5 and the third city can be chosen from the remaining 4.

Total number of sequences without restriction = 6 * 5 * 4 = 120

Number of ways the cities can be visited when both Stockholm and Oslo are visited in a single trip --> Assume there are 3 slots. Oslo can be visited in any of the 3 slots, Stockholm can be visited in any of the 2 remaining slots and the remaining slot can be chosen among 4 different cities --> Number of sequences = 3 * 2 * 4 = 24

Number of sequences the cities can be visited such that Oslo and Stockholm are not visited in a single trip = Total - Number of sequences the cities can be visited such that Stockholm and Oslo are visited in a single trip = 120 - 24 = 96.

I will be able to help you with my explanation for your comment.

The question asks for the number of sequences. Ex: Paris, Barcelona and Rome is one sequence. Paris, Rome and Barcelona is a different sequence. So the question tests you on permutations.

Without restriction, the first city to be visited can be chosen from any of the 6 given cities. The next city can be chosen from the remaining 5 and the third city can be chosen from the remaining 4.

Total number of sequences without restriction = 6 * 5 * 4 = 120

Number of ways the cities can be visited when both Stockholm and Oslo are visited in a single trip --> Assume there are 3 slots. Oslo can be visited in any of the 3 slots, Stockholm can be visited in any of the 2 remaining slots and the remaining slot can be chosen among 4 different cities --> Number of sequences = 3 * 2 * 4 = 24

Number of sequences the cities can be visited such that Oslo and Stockholm are not visited in a single trip = Total - Number of sequences the cities can be visited such that Stockholm and Oslo are visited in a single trip = 120 - 24 = 96.

Re: After a business trip to London, Michele has enough time to visit thre [#permalink]

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17 Sep 2016, 10:11

Vyshak wrote:

Hi

I will be able to help you with my explanation for your comment.

The question asks for the number of sequences. Ex: Paris, Barcelona and Rome is one sequence. Paris, Rome and Barcelona is a different sequence. So the question tests you on permutations.

Without restriction, the first city to be visited can be chosen from any of the 6 given cities. The next city can be chosen from the remaining 5 and the third city can be chosen from the remaining 4.

Total number of sequences without restriction = 6 * 5 * 4 = 120

Number of ways the cities can be visited when both Stockholm and Oslo are visited in a single trip --> Assume there are 3 slots. Oslo can be visited in any of the 3 slots, Stockholm can be visited in any of the 2 remaining slots and the remaining slot can be chosen among 4 different cities --> Number of sequences = 3 * 2 * 4 = 24

Number of sequences the cities can be visited such that Oslo and Stockholm are not visited in a single trip = Total - Number of sequences the cities can be visited such that Stockholm and Oslo are visited in a single trip = 120 - 24 = 96.

Hope it helps.

Why have you conveniently decided to place Oslo, and Stockholm first? What if I were to arrange in this way :

_ _ _ So I have three slots, the "other" city can be visited in any of those slots. Let's say I choose the first slot, then I have 4 options. With the second slot, I have only 2 options (either Oslo/Stockholm), and with the third I have only one. That gives a total of 8 ways.

Re: After a business trip to London, Michele has enough time to visit thre [#permalink]

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19 Sep 2016, 09:59

abhijeetkaushik wrote:

Vyshak wrote:

Hi

I will be able to help you with my explanation for your comment.

The question asks for the number of sequences. Ex: Paris, Barcelona and Rome is one sequence. Paris, Rome and Barcelona is a different sequence. So the question tests you on permutations.

Without restriction, the first city to be visited can be chosen from any of the 6 given cities. The next city can be chosen from the remaining 5 and the third city can be chosen from the remaining 4.

Total number of sequences without restriction = 6 * 5 * 4 = 120

Number of ways the cities can be visited when both Stockholm and Oslo are visited in a single trip --> Assume there are 3 slots. Oslo can be visited in any of the 3 slots, Stockholm can be visited in any of the 2 remaining slots and the remaining slot can be chosen among 4 different cities --> Number of sequences = 3 * 2 * 4 = 24

Number of sequences the cities can be visited such that Oslo and Stockholm are not visited in a single trip = Total - Number of sequences the cities can be visited such that Stockholm and Oslo are visited in a single trip = 120 - 24 = 96.

Hope it helps.

Why have you conveniently decided to place Oslo, and Stockholm first? What if I were to arrange in this way :

_ _ _ So I have three slots, the "other" city can be visited in any of those slots. Let's say I choose the first slot, then I have 4 options. With the second slot, I have only 2 options (either Oslo/Stockholm), and with the third I have only one. That gives a total of 8 ways.

You are restricting the 'others' to only first slot. You can initially place in any of the 3 slots. So it's 3 * 4 = 12.

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