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anonymous

  • 5 years ago

There are two rows of seats with three side-by-side seats in each row. Two little boys, two little girls, and two adults sit in the six seats so that neither little boy sits to the side of either little girl. In how many different ways can these six people be seated? OPTIONS 1) 48 2) 128 3) 192 4) 176

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  1. mattfeury
    • 5 years ago
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    I am inclined to think: \[2!^3 * 3! = 48 \]

  2. anonymous
    • 5 years ago
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    you have BBGGAA

  3. anonymous
    • 5 years ago
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    can we think in linear way??

  4. mattfeury
    • 5 years ago
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    what do you mean?

  5. anonymous
    • 5 years ago
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    how did you get that answer

  6. anonymous
    • 5 years ago
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    or kindely explain how u did?

  7. mattfeury
    • 5 years ago
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    if you a have of couple (2 people), you can arrange them in 2! ways. 2! = 2 * 1 = 2 if you have three couples in 3 rows, then they can be sat = \[2! * 2! * 2!\]

  8. mattfeury
    • 5 years ago
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    but! it can be: couple1 couple2 couple3 couple3 couple2 couple1 etc... so we can arrange the 3 couples in 3! ways.

  9. mattfeury
    • 5 years ago
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    so basically we have 6 seats. but first we simply that to three rows. we have three rows. a couple per row. there are 3! ways to arrange this. in each row, each couple can be arranged 2! ways. Since this is the case for each of the three rows, it is 2! * 2! * 2! multiplying all these possibilities together: 2! * 2! * 2! * 3! = 48

  10. anonymous
    • 5 years ago
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    you're treating the two boys as a couple?

  11. mattfeury
    • 5 years ago
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    ah yeah sorry. i was thinking of a similar problem with 3 couples. it is the same principle though. 3 sets of 2 individuals (in this case: boys, girls, adults).

  12. anonymous
    • 5 years ago
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    but you can rearrange the couples

  13. mattfeury
    • 5 years ago
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    yes. you can arrange the couples between the three rows. thus the 3!

  14. anonymous
    • 5 years ago
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    we have two rows _ _ _ _ _ _

  15. mattfeury
    • 5 years ago
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    ah i am so wrong. you are right.

  16. anonymous
    • 5 years ago
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    yes thats what m thinking .. how to solve its definitely not circular and I doubt on Linear permutation

  17. anonymous
    • 5 years ago
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    thats why i got confused about your answer

  18. mattfeury
    • 5 years ago
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    heh sorry. i misread the question :(. that's what i get for skimming.

  19. anonymous
    • 5 years ago
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    i will forgive you if you help me with my question, brb

  20. anonymous
    • 5 years ago
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    but go ahead and try to answer

  21. anonymous
    • 5 years ago
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    so you solved the question, 3 rows, boy cant sit next to girl?

  22. anonymous
    • 5 years ago
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    so i guess is it correct?? B1 B2 A1 ----6 WAYS G1 G2 A2 ----6 WAYS ie, TOTAL =36 ways

  23. mattfeury
    • 5 years ago
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    there is another set of cases: B1 A1 G1 B2 A2 G2

  24. mattfeury
    • 5 years ago
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    B1 A1 G1 = 2 ways to arrange B2 A2 G2 = 2 ways to arrange

  25. mattfeury
    • 5 years ago
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    better: B1 A1 G1 = 4 * 3 to arrange (you have a set of {b1, b2, g1, g2} and you have 4 and 3 options for the end) B2 A2 G2 = 2 * 1 ways to arrange

  26. mattfeury
    • 5 years ago
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    12 * 2 * 2 (another 2 to choose between the A's) = 48 for that case.

  27. mattfeury
    • 5 years ago
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    times another 2 to account for being able to switch the rows: r1, r2 or r2, r1

  28. mattfeury
    • 5 years ago
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    = 96 for that case. you'll have to + this to the possibilities for the other case

  29. mattfeury
    • 5 years ago
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    i may be wrong though. i can't seem to figure out the other case to where it adds to an answer :( 96 + (2 * 2 * 2 * 2) = 112?

  30. anonymous
    • 5 years ago
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    I am also confused dear :)

  31. mattfeury
    • 5 years ago
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    128 maybe!

  32. anonymous
    • 5 years ago
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    can it be like? B A G B A G G A B G A B B B A G G A G G A B B A A B B A G G A G G A B B Each case can be arranged in 8 ways , i.e. Boys - 2! , Gals - 2! , adults - 2! Hence 6 * (2*2*2) = 48 Option 1

  33. anonymous
    • 5 years ago
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    hi cantorset .. u ther??

  34. nowhereman
    • 5 years ago
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    The only possible cases are, if the girls sit on different rows, that the parents sit in the middle seats and the boys on the other sides. If the girls sit on the same row the third seat must be occupied by a parent and there is no further restriction on the other row. So you get for the number of constellations: In the first case 4*2!*2!*2! = 32 and in the second case 2*3*3*2!*2!*2! = 144, that means there are 176 possibilties.

  35. nowhereman
    • 5 years ago
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    need more explanation?

  36. anonymous
    • 5 years ago
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    yes i do, i got the same answer but i didnt get your 2x3x3x2! , etc

  37. nowhereman
    • 5 years ago
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    2 because the girls can either sit in the first or in the second row 3 because you can choose any seat in that row for the parent 3 because you must choose one seat in the other row where the second parent sits 2!*2!*2! always because it doesn't matter if you interchange the 2 girls / boys / parents with each other.

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