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# Two boys and four girls at a party will sit in a row. If two boys do

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BSchool Forum Moderator
Joined: 29 Jan 2015
Posts: 1475
Location: India
WE: General Management (Consumer Products)
Two boys and four girls at a party will sit in a row. If two boys do  [#permalink]

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01 Dec 2019, 11:49
2
00:00

Difficulty:

55% (hard)

Question Stats:

46% (01:36) correct 54% (02:20) wrong based on 28 sessions

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Two boys and four girls at a party will sit in a row. If two boys do not sit next to each other, how many seating arrangements are possible?

(A) 120

(B) 240

(C) 360

(D) 480

(E) 600
Intern
Joined: 18 Oct 2018
Posts: 2
Two boys and four girls at a party will sit in a row. If two boys do  [#permalink]

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01 Dec 2019, 12:55
1
1
Method 1

First the sitting arrangements are found.

_G_G_G_G_. In the case the arrangements for girls is 4!=4*3*2*1=24 as usual

Now there are 5 possible places ("_" between Girls) where boys can seat. In this case we will apply to combination 5C2= 5*4= 20
As a result, we have 24*20= 480

Method 2

Overal we have 6! possibilty. And if 2 boys sit togather we will have 5! such as (BB)GGGG or GGG(BB)GG and so on

The statement should be 6!-5!*2= 720-120*2= 480

Total number of ways in which 2 boys sit together - 6! 2! 2! ((BB)GGGG, we multiply by 2! once because 2 boys can interchange their place and we multiply 2!)
Senior Manager
Joined: 16 Feb 2015
Posts: 261
Location: United States
Concentration: Finance, Operations
Re: Two boys and four girls at a party will sit in a row. If two boys do  [#permalink]

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01 Dec 2019, 23:58
rohan2345 wrote:
Two boys and four girls at a party will sit in a row. If two boys do not sit next to each other, how many seating arrangements are possible?

(A) 120

(B) 240

(C) 360

(D) 480

(E) 600

Explanation:

Formula for these type of Questions: [(b+g)!−b!(g+1)!]

=6!−2!5!=480.

IMO-D

Please Give kudos, If you find my explanation good enough
Senior Manager
Joined: 16 Feb 2015
Posts: 261
Location: United States
Concentration: Finance, Operations
Re: Two boys and four girls at a party will sit in a row. If two boys do  [#permalink]

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02 Dec 2019, 00:00
rohan2345 wrote:
Two boys and four girls at a party will sit in a row. If two boys do not sit next to each other, how many seating arrangements are possible?

(A) 120

(B) 240

(C) 360

(D) 480

(E) 600

Another Method:

Consider 2 boys as a single unit.

So, possible ways of arranging 2 boys & 4 girls = arrangements such that 2 boys sit together = 5! = 120

Now ,since 2 boys are never to sit together , the number of required arrangements = 6! - (2*120) = 720 - 240 = 480

IMO-D

Please give kudos, If you find my explanation good enough
Re: Two boys and four girls at a party will sit in a row. If two boys do   [#permalink] 02 Dec 2019, 00:00
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# Two boys and four girls at a party will sit in a row. If two boys do

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