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anonymous

  • one year ago

In how many ways can the five letters J, K, L, M and N be arranged such that L is not in the middle?

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  1. anonymous
    • one year ago
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    i dont understand why it cant be 5 x 4 x 4 x 3 x 2

  2. sdfgsdfgs
    • one year ago
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    first u need to figure out: how many ways can 5 letters be arranged (including the cases where L is in the middle). what is that equal to?

  3. anonymous
    • one year ago
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    5!

  4. sdfgsdfgs
    • one year ago
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    Good job! :) Now consider this: how many ways can 4 letters, JKMN, be arranged in 4 positions? There are 4 open positions only because this assumes L is in the middle.

  5. anonymous
    • one year ago
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    wait it's not supposed to be in the middle

  6. sdfgsdfgs
    • one year ago
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    hehee go along w me there plz?

  7. anonymous
    • one year ago
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    So theres 4 ways?

  8. sdfgsdfgs
    • one year ago
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    missing a symbol after the 4 there...

  9. anonymous
    • one year ago
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    4!

  10. sdfgsdfgs
    • one year ago
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    Now what happens when u subtract this from the results u got before with 5 letters and 5 positions?

  11. anonymous
    • one year ago
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    huh?

  12. Plasmataco
    • one year ago
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    ok.

  13. Plasmataco
    • one year ago
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    how many positions can L BE IN the middle?

  14. anonymous
    • one year ago
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    0

  15. anonymous
    • one year ago
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    without = 4

  16. Plasmataco
    • one year ago
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    ...

  17. Plasmataco
    • one year ago
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    In JKLMN, L is in the middle.

  18. sdfgsdfgs
    • one year ago
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    ways 5 letters be arranged (including the cases where L is in the middle) = 5! ways 4 letters, JKMN, be arranged in 4 positions w/ L in the middle = 4! so 5!-4! = ways five letters J, K, L, M and N be arranged such that L is not in the middle

  19. anonymous
    • one year ago
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    hmmmm

  20. anonymous
    • one year ago
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    sorry im really not gettin it

  21. sdfgsdfgs
    • one year ago
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    @yomamabf think about it...or u can go along w the other way @Plasmataco is going :)

  22. anonymous
    • one year ago
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    wait i dont get why u would add L in the middle?

  23. anonymous
    • one year ago
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    when it says not to

  24. sdfgsdfgs
    • one year ago
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    so that those cases (4!) can be SUBTRACTED from the others (5!)

  25. anonymous
    • one year ago
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    why do u subtract it

  26. sdfgsdfgs
    • one year ago
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    cuz' u are trying to find ways that L is NOT in the middle ;)

  27. anonymous
    • one year ago
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    wouldnt it just be 5 x 4 x 4 x 3 x 2?

  28. sdfgsdfgs
    • one year ago
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    total cases = (cases L in middle) + (cases L not in the middle) n ur prob is asking u to find (cases L not in the middle)

  29. anonymous
    • one year ago
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    so subtract it huh

  30. sdfgsdfgs
    • one year ago
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    Correct - the other way is to directly calculate (cases L not in the middle) n i think that was where the other helper was going.

  31. anonymous
    • one year ago
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    how do u do that method?

  32. sdfgsdfgs
    • one year ago
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    hahahaaa its slightly more complicated n dats why i did it my way...perhaps u can ask @Plasmataco to come back n show u? :)

  33. sdfgsdfgs
    • one year ago
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    OK.... for L not in the middle, it will be: L _ _ _ _ or _ L _ _ _ or _ _ _ L _ or _ _ _ _ L so far so good?

  34. anonymous
    • one year ago
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    yes

  35. ybarrap
    • one year ago
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    Here are all the ways to permute the 4 letters {J, K, M, N} | {J, K, N, M} | {J, M, K, N} | {J, M, N, K} | {J, N, K, M} | {J, N, M, K} | {K, J, M, N} | {K, J, N, M} | {K, M, J, N} | {K, M, N, J} | {K, N, J, M} | {K, N, M, J} | {M, J, K, N} | {M, J, N, K} | {M, K, J, N} | {M, K, N, J} | {M, N, J, K} | {M, N, K, J} | {N, J, K, M} | {N, J, M, K} | {N, K, J, M} | {N, K, M, J} | {N, M, J, K} | {N, M, K, J} (total: 4!=24) 4! places to permute J,K,M,N, while keeping L in the middle is the same as permuting just J,K,M,N because L has no freedom to permute to another position. There are 5! ways to permute all the letters (see below) Here are all the ways to permute the 5 letters. Count the ones with L in the Middle, there will be 24. The remaining will be those permutations without L in the middle. That's why you subtract: 5! - 4!. It's easier to count those without L in the middle then subtract than to directly count those with L in the middle. {J, K, L, M, N} | {J, K, L, N, M} | {J, K, M, L, N} | {J, K, M, N, L} | {J, K, N, L, M} | {J, K, N, M, L} | {J, L, K, M, N} | {J, L, K, N, M} | {J, L, M, K, N} | {J, L, M, N, K} | {J, L, N, K, M} | {J, L, N, M, K} | {J, M, K, L, N} | {J, M, K, N, L} | {J, M, L, K, N} | {J, M, L, N, K} | {J, M, N, K, L} | {J, M, N, L, K} | {J, N, K, L, M} | {J, N, K, M, L} | {J, N, L, K, M} | {J, N, L, M, K} | {J, N, M, K, L} | {J, N, M, L, K} | {K, J, L, M, N} | {K, J, L, N, M} | {K, J, M, L, N} | {K, J, M, N, L} | {K, J, N, L, M} | {K, J, N, M, L} | {K, L, J, M, N} | {K, L, J, N, M} | {K, L, M, J, N} | {K, L, M, N, J} | {K, L, N, J, M} | {K, L, N, M, J} | {K, M, J, L, N} | {K, M, J, N, L} | {K, M, L, J, N} | {K, M, L, N, J} | {K, M, N, J, L} | {K, M, N, L, J} | {K, N, J, L, M} | {K, N, J, M, L} | {K, N, L, J, M} | {K, N, L, M, J} | {K, N, M, J, L} | {K, N, M, L, J} | {L, J, K, M, N} | {L, J, K, N, M} | {L, J, M, K, N} | {L, J, M, N, K} | {L, J, N, K, M} | {L, J, N, M, K} | {L, K, J, M, N} | {L, K, J, N, M} | {L, K, M, J, N} | {L, K, M, N, J} | {L, K, N, J, M} | {L, K, N, M, J} | {L, M, J, K, N} | {L, M, J, N, K} | {L, M, K, J, N} | {L, M, K, N, J} | {L, M, N, J, K} | {L, M, N, K, J} | {L, N, J, K, M} | {L, N, J, M, K} | {L, N, K, J, M} | {L, N, K, M, J} | {L, N, M, J, K} | {L, N, M, K, J} | {M, J, K, L, N} | {M, J, K, N, L} | {M, J, L, K, N} | {M, J, L, N, K} | {M, J, N, K, L} | {M, J, N, L, K} | {M, K, J, L, N} | {M, K, J, N, L} | {M, K, L, J, N} | {M, K, L, N, J} | {M, K, N, J, L} | {M, K, N, L, J} | {M, L, J, K, N} | {M, L, J, N, K} | {M, L, K, J, N} | {M, L, K, N, J} | {M, L, N, J, K} | {M, L, N, K, J} | {M, N, J, K, L} | {M, N, J, L, K} | {M, N, K, J, L} | {M, N, K, L, J} | {M, N, L, J, K} | {M, N, L, K, J} | {N, J, K, L, M} | {N, J, K, M, L} | {N, J, L, K, M} | {N, J, L, M, K} | {N, J, M, K, L} | {N, J, M, L, K} | {N, K, J, L, M} | {N, K, J, M, L} | {N, K, L, J, M} | {N, K, L, M, J} | {N, K, M, J, L} | {N, K, M, L, J} | {N, L, J, K, M} | {N, L, J, M, K} | {N, L, K, J, M} | {N, L, K, M, J} | {N, L, M, J, K} | {N, L, M, K, J} | {N, M, J, K, L} | {N, M, J, L, K} | {N, M, K, J, L} | {N, M, K, L, J} | {N, M, L, J, K} | {N, M, L, K, J} (total: 5!=120)

  36. sdfgsdfgs
    • one year ago
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    OK now consider the first case L _ _ _ _ how ways are there to fill KJMN to the 4 spaces?

  37. anonymous
    • one year ago
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    i get it now thanks

  38. sdfgsdfgs
    • one year ago
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    ok :)

  39. ybarrap
    • one year ago
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    You're welcome

  40. anonymous
    • one year ago
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    4 x 3 x 4 x 2 x 1 = 96 You use the 4 in the beginning because the middle letter is already used by a letter other than L so it cant be a 5 in the beginning

  41. sdfgsdfgs
    • one year ago
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    @yomamabf correct - then if u consider there are 4 ways: L _ _ _ _ or _ L _ _ _ or _ _ _ L _ or _ _ _ _ L So the ans becomes 4*4! which is equal to 5!-4!

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