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Bunuel
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A fast-food company plans to build four new restaurants. If there are 12 Apr 2021, 02:45
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70% (02:05) correct 30% (01:43) wrong based on 163 sessions

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A fast-food company plans to build four new restaurants. If there are six sites A, B, C, D, E and F, that satisfy the company’s criteria for location of the new restaurants, in how many different ways can the company select four sites if the order of selection does not matter, given that both the sites A and B cannot be selected simultaneously?

(A) 4
(B) 5
(C) 6
(D) 9
(E) 15
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D
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A fast-food company plans to build four new restaurants. If there are 12 Apr 2021, 02:53
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Total ways of selecting 4 cities out of 6=6c2
Ways of selecting A and B and any other two cities= 1*4c2
Ways of selecting 4 cities and excluding selection of A&B together= 6C2- 4C2=9
Option D
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A fast-food company plans to build four new restaurants. If there are 14 Aug 2021, 21:06
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sumitkrocks
Total ways of selecting 4 cities out of 6=6c2
Ways of selecting A and B and any other two cities= 1*4c2
Ways of selecting 4 cities and excluding selection of A&B together= 6C2- 4C2=9
Option D
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i can't understand why you write 6c2 else 6c4??

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A fast-food company plans to build four new restaurants. If there are 14 Aug 2021, 21:16
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Total cities = 6

Select 4 out of 6: \(^6{C_4} = ^6{C_2} = 15\)

There is 1 way to select A and B together and remaining 2 cities will be selected from 4: \(^4{C_2} = 6 = 1 * 6 = 6\)

A and B not together: 15 - 6 = 9

Answer D
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A fast-food company plans to build four new restaurants. If there are 15 Aug 2021, 06:42
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Bunuel
A fast-food company plans to build four new restaurants. If there are six sites A, B, C, D, E and F, that satisfy the company’s criteria for location of the new restaurants, in how many different ways can the company select four sites if the order of selection does not matter, given that both the sites A and B cannot be selected simultaneously?

(A) 4
(B) 5
(C) 6
(D) 9
(E) 15
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The total ways of selecting 4 cities = 15 or 6c4

The total ways of chosing with A and B chosen = 1*4c2=6

Therefore total way of chosing without picking Aand B = 15-6 =9

Therefore IMO D
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A fast-food company plans to build four new restaurants. If there are 27 Aug 2021, 23:10
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Bunuel
A fast-food company plans to build four new restaurants. If there are six sites A, B, C, D, E and F, that satisfy the company’s criteria for location of the new restaurants, in how many different ways can the company select four sites if the order of selection does not matter, given that both the sites A and B cannot be selected simultaneously?

(A) 4
(B) 5
(C) 6
(D) 9
(E) 15
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IMO D

Choose 4 sites from the given 6: A,B,C,D,E,F
A & B cannot be together in a chosen set

Option 1: A _ _ _ -> 4C3 ways to fill the remaining spots = 4 ways
Option 2: B _ _ _ -> 4C3 ways to fill the remaining spots = 4 ways
Option 3 (No A & B) : _ _ _ _ -> Only have 1 way (C,D,E,F in any order)

So, 4+4+1 = 9 ways
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A fast-food company plans to build four new restaurants. If there are 02 Jun 2022, 08:55
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My 2 cents on this:

Note down every aspect. 6 locations/sites and 4 restaurants. Total? 6c4= 15 (Therefore answer cannot be E ever)

Then, we are given the condition, A&B cannot be together. So if we equate Total - A&B together = A&B Not together.

A&B together is straightforward. Consider AB is a block that cannot be separated. AB | CDEF are the blocks. AB will give us 2 restaurants. 2c2. Then CDEF will give us 4c2 = 6

So 15-6 = 9 is the answer.

Tricky, but I'm trying to implement this more and more.
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