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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?
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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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i dont understand why it cant be 5 x 4 x 4 x 3 x 2

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1first 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?

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1Good 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.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait it's not supposed to be in the middle

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1hehee go along w me there plz?

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1missing a symbol after the 4 there...

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1Now what happens when u subtract this from the results u got before with 5 letters and 5 positions?

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0how many positions can L BE IN the middle?

Plasmataco
 one year ago
Best ResponseYou've already chosen the best response.0In JKLMN, L is in the middle.

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1ways 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

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0sorry im really not gettin it

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1@yomamabf think about it...or u can go along w the other way @Plasmataco is going :)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wait i dont get why u would add L in the middle?

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1so that those cases (4!) can be SUBTRACTED from the others (5!)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why do u subtract it

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1cuz' u are trying to find ways that L is NOT in the middle ;)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wouldnt it just be 5 x 4 x 4 x 3 x 2?

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1total 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)

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1Correct  the other way is to directly calculate (cases L not in the middle) n i think that was where the other helper was going.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do u do that method?

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1hahahaaa its slightly more complicated n dats why i did it my way...perhaps u can ask @Plasmataco to come back n show u? :)

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1OK.... for L not in the middle, it will be: L _ _ _ _ or _ L _ _ _ or _ _ _ L _ or _ _ _ _ L so far so good?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Here 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)

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1OK now consider the first case L _ _ _ _ how ways are there to fill KJMN to the 4 spaces?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.04 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

sdfgsdfgs
 one year ago
Best ResponseYou've already chosen the best response.1@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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