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Gerald and his family are at point A when they receive an alert that a

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Gerald and his family are at point A when they receive an alert that a  [#permalink]

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New post 27 Nov 2019, 01:31
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A
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C
D
E

Difficulty:

  35% (medium)

Question Stats:

52% (01:34) correct 48% (01:29) wrong based on 25 sessions

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Gerald and his family are at point A when they receive an alert that a cloud of poisonous gas is moving toward them from the southwest. They need to avoid the cloud of gas by driving to a shelter at point B. If they must stay on the grid and are only able to drive north and east, how many different routes can they take from point A to point B?

A. 12
B. 15
C. 21
D. 30
E. 35

Attachment:
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Re: Gerald and his family are at point A when they receive an alert that a  [#permalink]

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New post 27 Nov 2019, 05:30
Total number of ways = (4+3)!/4!3!= 35

Bunuel wrote:
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Gerald and his family are at point A when they receive an alert that a cloud of poisonous gas is moving toward them from the southwest. They need to avoid the cloud of gas by driving to a shelter at point B. If they must stay on the grid and are only able to drive north and east, how many different routes can they take from point A to point B?

A. 12
B. 15
C. 21
D. 30
E. 35

Attachment:
grid.jpg
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Re: Gerald and his family are at point A when they receive an alert that a  [#permalink]

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New post 27 Nov 2019, 07:41
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Bunuel wrote:
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Gerald and his family are at point A when they receive an alert that a cloud of poisonous gas is moving toward them from the southwest. They need to avoid the cloud of gas by driving to a shelter at point B. If they must stay on the grid and are only able to drive north and east, how many different routes can they take from point A to point B?

A. 12
B. 15
C. 21
D. 30
E. 35

Attachment:
grid.jpg


Key point: Regardless of how Gerald gets from point A to point B, his path will always consist of driving three blocks north and four blocks east.

For example, one possible route might be represented by: NNNEEEE
Here Gerald drives north for a block, north for another block, north for another block, and then east for four blocks.

Another possible route might be: NEENNEE, etc

So the question really comes down to " in how many different ways can we arrange three N's and 4 E's?"

----ASIDE-------------------
When we want to arrange a group of items in which some of the items are identical, we can use something called the MISSISSIPPI rule. It goes like this:

If there are n objects where A of them are alike, another B of them are alike, another C of them are alike, and so on, then the total number of possible arrangements = n!/[(A!)(B!)(C!)....]

So, for example, we can calculate the number of arrangements of the letters in MISSISSIPPI as follows:
There are 11 letters in total
There are 4 identical I's
There are 4 identical S's
There are 2 identical P's
So, the total number of possible arrangements = 11!/[(4!)(4!)(2!)]
--------------------------

Back to the question.
We want to arrange the letters in the word NNNEEEE
There are 7 letters in total
There are 4 identical E's
There are 3 identical N's
So, the total number of possible arrangements = 7!/[(4!)(3!)]
= (7)(6)(5)(4)(3)(2)(1)/(4)(3)(2)(1)(3)(2)(1)
= (7)(6)(5)/(3)(2)(1)
= (7)(5)
= 35

Answer: E

Cheers,
Brent
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Re: Gerald and his family are at point A when they receive an alert that a   [#permalink] 27 Nov 2019, 07:41
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