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A fast food company plans to build 4 new restaurants. If there are 12

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Bunuel
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A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  16 Oct 2016, 03:03
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A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.

A. 48
B. 288
C. 495
D. 990
E. 11880
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  16 Oct 2016, 03:13
Bunuel wrote:
A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant,in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.

A. 48
B. 288
C. 495
D. 990
E. 11880


\(12C4 = 495\)

Answer will be (C) 495
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Gordon2701
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  16 Oct 2016, 03:23
Bunuel wrote:
A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.

A. 48
B. 288
C. 495
D. 990
E. 11880


I think the answer is C. It's a combinatorics problem, since the order of the selection does not matter. Therefore 4 sites can be selected from the 12 sites available in \(\frac{12*11*10*9}{1*2*3*4}\), or 495 different ways.
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  16 Oct 2016, 18:50
12C4 , C is the answer
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  16 Oct 2016, 21:26
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Bunuel wrote:
A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.

A. 48
B. 288
C. 495
D. 990
E. 11880


The number of ways of choosing 4 sites out of 12 are counted by = 12C4 ways = 495

Answer: Option C
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  01 Nov 2016, 02:38
We have to select 4 restaurants from a total of 12 restaurants (order doesn't matter)
selecting 4 out of 12 = 12 C 4 = \(\frac{12!}{4!*8!}\) = 495
Correct answer - C
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  17 Aug 2021, 01:00
The answer is definitely C
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  17 Aug 2021, 21:47
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Number of ways to select 4 out of 12 sites is 12 C 4

= 12! / 4! * 8!

=495

(option c)

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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink] New post  18 Dec 2023, 05:35
Bunuel wrote:
A fast food company plans to build 4 new restaurants. If there are 12 sites that satisfy the company's criteria for location of new restaurant, in how many different ways can company select the 4 sites needed for the new restaurant if the order of selection doesn't matter.

A. 48
B. 288
C. 495
D. 990
E. 11880


I know this might sound dumb and I understand why the answer is C, 495.
But could someone explain why it is not 11 880 : Considering that for:
Choice available for the first site: 12 options * Choice available for the second site: 11 options * Choice available for the third site: 10 options* Choice available for the 4th site: 9 options.
Therefore: 12*11*10*9 = 11 880 different ways to arrange the sites for the restaurant.
Thank you for your help !
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Re: A fast food company plans to build 4 new restaurants. If there are 12 [#permalink]
18 Dec 2023, 05:35
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