There are 5 cars to be displayed in 5 parking spaces with all the cars facing direction. Of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. If the cars are identical except for the color, how many different display arrangement of the 5 cars are possible?
a - 20
b - 25
c - 40
d - 60
e - 125
I reached to C - 40 but OA - 20. I assumed that car be parked in two direction - up and down. I am right in the assumption.
Thanks
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tanviet
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suppose 5 car are diferent, according to princeton book, there will be
5.4.3.2.1= ways to arrange.
there will be
3.2.1=ways to arrage 3 cars
if these 3 cars are the same, 3.2.1=ways will be the same. this case happens with the red
so we have to divide
5.4.3.2.1/3.2.1 =20
oa A.
5.4.3.2.1= ways to arrange.
there will be
3.2.1=ways to arrage 3 cars
if these 3 cars are the same, 3.2.1=ways will be the same. this case happens with the red
so we have to divide
5.4.3.2.1/3.2.1 =20
oa A.
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GMATGuruNY
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The number of ways to arrange 5 DISTINCT elements = 5! = 120.ashg84 wrote:There are 5 cars to be displayed in 5 parking spaces with all the cars facing direction. Of the 5 cars, 3 are red, 1 is blue, and 1 is yellow. If the cars are identical except for the color, how many different display arrangement of the 5 cars are possible?
a - 20
b - 25
c - 40
d - 60
e - 125
But here, the 3 red cars are IDENTICAL.
When identical elements swap positions, the arrangement doesn't change, reducing the total number of unique arrangements.
To account for the duplicate arrangements, we DIVIDE by the number of ways to ARRANGE the identical elements.
The number of ways to arrange the 3 red cars = 3!.
Thus:
5!/3! = 20.
The correct answer is A.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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