A restaurant is hanging 7 large tiles on its wall in a single row : Problem Solving (PS)

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A restaurant is hanging 7 large tiles on its wall in a single row

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Senior Manager

Joined: 02 Jan 2017

Posts: 293

Location: Canada

A restaurant is hanging 7 large tiles on its wall in a single row [#permalink]

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17 Feb 2017, 16:37

00:00

Difficulty:

15% (low)

Question Stats:

78% (01:07) correct

22% (01:51) wrong

based on 82 sessions

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A restaurant is hanging 7 large tiles on its wall in a single row. How many arrangements of tiles are possible if there are 3 white tiles and 4 blue tiles?

A. 35
B. 12
C. 21
D. 84
E. 28

Spoiler: OA

Math Expert

Joined: 02 Aug 2009

Posts: 7991

Re: A restaurant is hanging 7 large tiles on its wall in a single row [#permalink]

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17 Feb 2017, 19:40

vikasp99 wrote:

A restaurant is hanging 7 large tiles on its wall in a single row. How many arrangements of tiles are possible if there are 3 white tiles and 4 blue tiles?

A. 35
B. 12
C. 21
D. 84
E. 28

Hi..

Total ways these 7 tiles can be arranged =7!
However these contain duplicity as 3 tiles are of one colour and other 4 are of other colour..
So eliminating these = \(\frac{7!}{3!4!}\)=35

A
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Senior Manager

Joined: 17 Mar 2014

Posts: 429

Re: A restaurant is hanging 7 large tiles on its wall in a single row [#permalink]

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20 Jan 2019, 08:21

vikasp99 wrote:

A restaurant is hanging 7 large tiles on its wall in a single row. How many arrangements of tiles are possible if there are 3 white tiles and 4 blue tiles?

A. 35
B. 12
C. 21
D. 84
E. 28

Hello Bunuel,

Isn't this question confusing. 3 White tiles could be different white tiles and/or 4 blue tiles could be different blue tiles ? How we can make sure that all white/blue tiles are similar ?

Thanks,
Amm

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Joined: 15 Feb 2018

Posts: 367

Re: A restaurant is hanging 7 large tiles on its wall in a single row [#permalink]

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20 Jan 2019, 17:59

ammuseeru
I understand your attention to detail (based on some convoluted and tricky gmat questions), but it I have not found it necessary for combination questions. Most people (including and especially me) find this section confusing. The questions ask straight forward questions and simply require application of rules. This question tests 'permutation with repeated elements'.

\(P(n; n_1, n_2, . . . , n_k) = \frac{n!}{n_1! n_2! . . . n_k!}\)