anonymous
  • anonymous
In how many arrangements can 3 boys and 4 girls stand in a row such that no two boys are together?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
@ganeshie8 @ParthKohli @AriPotta
ParthKohli
  • ParthKohli
Number of ways that they can stand in - number of ways two boys can stand together. Note that the latter also covers the number of ways in which three boys can stand together.
ParthKohli
  • ParthKohli
Oh, and also keep in mind that they can permute among themselves, like @ganeshie8 spotted the last time.

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More answers

anonymous
  • anonymous
I got 5040 at total number of ways they can stand together
anonymous
  • anonymous
How would you calculate the number of ways two boys can stand together? I feel like I am messing up there
ParthKohli
  • ParthKohli
Just like you did the last time.
ParthKohli
  • ParthKohli
Oh, and yes, you have three boys, so you also need to see that you can choose any 2 out of 3 boys.
anonymous
  • anonymous
See I messed up somewhere I got 5028...
ganeshie8
  • ganeshie8
4 girls can be arranged in 4! after that, 3 boys can be inserted in between the boys in 5C3 * 3! ways so in total we have 4! * 5C3*3! = 1440 ways
anonymous
  • anonymous
720 4,320 3,600 4,000
ParthKohli
  • ParthKohli
Why 5C3?
ParthKohli
  • ParthKohli
\[7! - 2 \cdot \binom{3}{2}\cdot 6!\]
ganeshie8
  • ganeshie8
place girls in the blanks first |dw:1432838542055:dw|
ParthKohli
  • ParthKohli
Oh, I see.
ganeshie8
  • ganeshie8
after that, we have 5 places for placing boys |dw:1432838582145:dw|
anonymous
  • anonymous
but 1440 is not an option. so what is wrong?
ParthKohli
  • ParthKohli
Is 720 correct? Just wondering...
anonymous
  • anonymous
720 is an option
ParthKohli
  • ParthKohli
Is the option correct?
anonymous
  • anonymous
I dont think so?
ParthKohli
  • ParthKohli
What's the correct one?
anonymous
  • anonymous
Im not sure :/
ganeshie8
  • ganeshie8
i don't see how it cannot be 1440
anonymous
  • anonymous
1440 is that arrangement is the only the girls are sitting on the end seats
anonymous
  • anonymous
Pattern: gbgbgbg # of arrangements: 4!*3! = 144
ganeshie8
  • ganeshie8
girls need not be in the ends |dw:1432839047302:dw|
anonymous
  • anonymous
# of ways to fill the end seats: 4*3 = 12 # of ways to fill the other 5 seats: 5! # of arrangements: 12*5! = 1440
anonymous
  • anonymous
yeah :/ I am getting the same way... but this is not an answer...
ganeshie8
  • ganeshie8
as the question stands, 1440 is the correct answer it just so happens that the options don't have the correct answer... inform ur teacher and move on to next q

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