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In how many ways can the letters of the word PENCILS be arranged in a row so that the L precedes the N? (Answer = 2520)
I am... really confused with this one.
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There only exist two situation , L precdeds the N , or N precedes the L ,that means there are only half of the arrangement satisfy the need , the total arrangements 7! , then the satifying arrangement is 7!/2 =2520
Numbers are the essence of the Universe
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Oh... I see. Thanks Stanley, I hadn't noticed that.
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you're welcome. I just happen to have an inspiration,hehe
Last edited by Stanley_Marsh (2006-12-23 04:10:12)
Numbers are the essence of the Universe
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You'd be surprised how much factorials pop up.
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That was a tricky one.
It gave me inspiration,too.
Try with the word PENCILLS.
I can rephrase the Stanley's solution:
Let S be the set of all words.
We have 2 sets of words:
A)..xxNx..xLxx..
B)..xxLx..xNxx..
Then A U B = S and A . B = {} (here "." stands for 'or')
And, there exists a bijection θ: A->B, so |A|=|B|.
We can use simular observations to prove the following theorem:
Let
Last edited by krassi_holmz (2006-12-24 06:44:14)
IPBLE: Increasing Performance By Lowering Expectations.
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