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Consider watching cars on the the highway

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logann2
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Consider watching cars on the the highway [#permalink] New post   07 Sep 2019, 12:53
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Consider watching cars on the highway. Each car can either turn left (L), right (R), or go straight (S). How many possible combinations are there where exactly 2 cars go in the same direction?

Source: Based off a questions in "Probability with Applications in Engineering, Science, and Technology" (Carlton, Devore)
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Re: Consider watching cars on the the highway [#permalink] New post   07 Sep 2019, 13:11
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logann2 wrote:
Consider watching cars on the highway. Each car can either turn left (L), right (R), or go straight (S).
How many possible combinations are there where exactly 2 cars go in the same direction?

Source: Based off a questions in "Probability with Applications in Engineering, Science, and Technology" (Carlton, Devore)


Here's how I did it...

We have 3 spots. We can choose 2 of them to be the same. 3C2. Then that group can choose from 3 options for what they'll do. 3C1. The remaining spot can't repeat so it can only choose 1 of 2 options. 2C1.

Thus we have 3C2*3C1*2C1 which evaluates to 18.
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Re: Consider watching cars on the the highway [#permalink] New post   14 Sep 2019, 04:56
how did you do the first " 3C2 "? The question doesn't mention we have three cars ? only two cars
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Re: Consider watching cars on the the highway [#permalink] New post   14 Sep 2019, 08:27
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3 are not the car . They are the directions that they could get on a highway.

read carefully the stem.

Regards
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Re: Consider watching cars on the the highway [#permalink] New post   15 Sep 2019, 20:46
logann2 wrote:
logann2 wrote:
Consider watching cars on the highway. Each car can either turn left (L), right (R), or go straight (S).
How many possible combinations are there where exactly 2 cars go in the same direction?

Source: Based off a questions in "Probability with Applications in Engineering, Science, and Technology" (Carlton, Devore)


Here's how I did it...

We have 3 spots. We can choose 2 of them to be the same. 3C2. Then that group can choose from 3 options for what they'll do. 3C1. The remaining spot can't repeat so it can only choose 1 of 2 options. 2C1.

Thus we have 3C2*3C1*2C1 which evaluates to 18.


I'm thinking of it this way: I have two cars because they will go to 1 direction I will consider them 1. Then they have 3 options they will take 1. 3C1. Why the answer as above ?
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Re: Consider watching cars on the the highway [#permalink] New post   16 Sep 2019, 03:54
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Asmakan wrote:
logann2 wrote:
logann2 wrote:
Consider watching cars on the highway. Each car can either turn left (L), right (R), or go straight (S).
How many possible combinations are there where exactly 2 cars go in the same direction?

Source: Based off a questions in "Probability with Applications in Engineering, Science, and Technology" (Carlton, Devore)


Here's how I did it...

We have 3 spots. We can choose 2 of them to be the same. 3C2. Then that group can choose from 3 options for what they'll do. 3C1. The remaining spot can't repeat so it can only choose 1 of 2 options. 2C1.

Thus we have 3C2*3C1*2C1 which evaluates to 18.


I'm thinking of it this way: I have two cars because they will go to 1 direction I will consider them 1. Then they have 3 options they will take 1. 3C1. Why the answer as above ?



First::There are no mention of cars - it can be infinite number of cars.

But, we were given 3 direction, where the car can move.

Next, we need to find in how many ways cars can travel in exactly 2 direction i.e Left & Right , Left & Straight , Right & Straight

After u ve analysed the ques, now it's time to combine the possible ways.

STEP 1:

We ve 3 direction (LEFT, RIGHT & STRAIGHT) but we need exactly 2 : So this can be found by 3C2 ways

STEP 2:

Now we got 3 options to choose from Left & Right , Left & Straight , Right & Straight ; This can be found by 3C1 ( because we can only choose one option out of 3)

Step 3::

Next we only have got one option left to choose from 2 i,e ( if we have selected LEFT & RIGHT - one direction is already chosen and we are left with only one option) This can be found : 2C1 ways

Now combine them, you will get the answer.
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Re: Consider watching cars on the the highway [#permalink] New post   30 Oct 2019, 20:51
Here's how I did it...

We have 3 spots. We can choose 2 of them to be the same. 3C2. Then that group can choose from 3 options for what they'll do. 3C1. The remaining spot can't repeat so it can only choose 1 of 2 options. 2C1.

Thus we have 3C2*3C1*2C1 which evaluates to 18.
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Re: Consider watching cars on the the highway [#permalink] New post   03 Nov 2019, 08:53
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Re: Consider watching cars on the the highway [#permalink] New post   29 Jul 2022, 06:20
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