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kryton1212 Group Title

4 boys and 4 girls are arranged to sit in a row. Find the number of arrangements that can be made if : (a) there is no restriction, >>>(4+4)!=40320<<< (b) the boys must sit separately, >>>4!*4!=576<<< (c) 2 girls must sit at the ends. >>>(8-1)!*2!=10080<<< is it correct?

  • 11 months ago
  • 11 months ago

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  1. kryton1212 Group Title
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    @ganeshie8

    • 11 months ago
  2. ganeshie8 Group Title
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    a is correct b think again c wrong

    • 11 months ago
  3. ganeshie8 Group Title
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    for b :- (b) the boys must sit separately, tie all 4 boys in one bag remaining 4 girls separate. so total 1 bag + 4 girls = 5 objects can be permuted in 5! ways boys inside bag can be permuted in 4! ways so total arrangements = 5!*4!

    • 11 months ago
  4. kryton1212 Group Title
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    oh i see...

    • 11 months ago
  5. kryton1212 Group Title
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    how about part c then?

    • 11 months ago
  6. RolyPoly Group Title
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    Errr, how can you tie all boys in one bag if all boys must sit separately in part b?

    • 11 months ago
  7. kryton1212 Group Title
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    @ganeshie8

    • 11 months ago
  8. RolyPoly Group Title
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    When boy must sit separately, girls must also sit separately, e.g.: B G B G B G B G Then 4!4! is correct for this case. That's one arrangement. But you can also have a girl taking the first seat, i.e. G B G B G B G B So, you need to multiply your original answer by two.

    • 11 months ago
  9. RolyPoly Group Title
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    When two girls must sit at two ends, you have: \(G_1, x, x, x, x, x, x, G_2\) So, you need to permute the 6 x's and the two G'.

    • 11 months ago
  10. kryton1212 Group Title
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    i understand your point. but i am still confusing part b and c...

    • 11 months ago
  11. RolyPoly Group Title
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    Which part(s) are you confused at?

    • 11 months ago
  12. kryton1212 Group Title
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    b and c

    • 11 months ago
  13. RolyPoly Group Title
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    I mean what..

    • 11 months ago
  14. kryton1212 Group Title
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    why tie in a bag is wrong?

    • 11 months ago
  15. RolyPoly Group Title
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    When you tie them together, they are connected and are no longer seperated, i.e. You take A = B B B B, and you arrange A G G G G

    • 11 months ago
  16. kryton1212 Group Title
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    oh yes.

    • 11 months ago
  17. RolyPoly Group Title
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    Clear?

    • 11 months ago
  18. kryton1212 Group Title
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    clear. so what should we do in this case?

    • 11 months ago
  19. RolyPoly Group Title
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    ?

    • 11 months ago
  20. kryton1212 Group Title
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    i mean, what should be the correct working step?

    • 11 months ago
  21. RolyPoly Group Title
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    Read above comments

    • 11 months ago
  22. kryton1212 Group Title
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    i cannot understand 6 x.

    • 11 months ago
  23. RolyPoly Group Title
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    That's part c,right?

    • 11 months ago
  24. kryton1212 Group Title
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    i got part b now. and go on to part c

    • 11 months ago
  25. RolyPoly Group Title
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    Those x's are either boys or girls.

    • 11 months ago
  26. RolyPoly Group Title
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    You only need to fix two girls (of course you need to permute that two girls as well) at the end, the others, you can mix and match, let the rest permute themselves.

    • 11 months ago
  27. digitalmonk Group Title
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    when two girls sit in the two ends they can do it in 2 ways so remaining 4 boys and 2 girls = 6 students can sit in 6! = 720 ways total no of ways = 2x720 = 1440

    • 11 months ago
  28. kryton1212 Group Title
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    oh, i made it as (8-1)!*2! ... understand now...i forgot 2 girls must sit at the ends....

    • 11 months ago
  29. digitalmonk Group Title
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    :)

    • 11 months ago
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