digit problem

For discussing Olympiad Level Combinatorics problems
the arrivals
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digit problem

Unread post by the arrivals » Thu Dec 23, 2010 12:04 pm

How many 10 letter words are there in which each of the letters contain a,v,i,k
1) at most once??
2)at least once??
to the admin: do i need to download any software to use latex? i cant make it.(sorry and will remain grateful if you please again do give the instruction )
the arrivals
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Moon
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Re: digit problem

Unread post by Moon » Thu Dec 23, 2010 6:12 pm

I am surprised that you did not notice the first few lines that I wrote in the forum home page.
You should get every instruction to start from there.
BTW the links on my signature (below my post) will also answer all your questions.
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

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Labib
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Re: digit problem

Unread post by Labib » Sat Dec 25, 2010 11:35 pm

I don't really understand the ques!!
but Here are the sol'ns I made of what I made out of the probs!
$1$) $26^4\times 4^6$
$2$) $22^6\times 4^4$

Please confirm if I'm right??
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HandaramTheGreat
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Re: digit problem

Unread post by HandaramTheGreat » Sun Dec 26, 2010 12:04 pm

the second one is $26^{10}-22^{10}$...

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Labib
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Re: digit problem

Unread post by Labib » Sun Dec 26, 2010 11:08 pm

Bonji, Plz give ur sol'n.

Btw I see my prob. my sol'n for the 2nd prob should have been $26^4 \times 22^6$
Is my sol'n also ok??
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Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

HandaramTheGreat
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Re: digit problem

Unread post by HandaramTheGreat » Mon Dec 27, 2010 11:31 am

AT LEAST once=(total permutation) - (those words which haven't a,v,i,k)

it's not ok :(

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Labib
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Re: digit problem

Unread post by Labib » Mon Dec 27, 2010 10:40 pm

Yeah! I saw that last night while spending an hour after thinking about the combi probs I've been working on last week. I also found out that u've become a mastermind of combi probs, bonji!! :D
Please Install $L^AT_EX$ fonts in your PC for better looking equations,
Learn how to write equations, and don't forget to read Forum Guide and Rules.


"When you have eliminated the impossible, whatever remains, however improbable, must be the truth." - Sherlock Holmes

HandaramTheGreat
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Re: digit problem

Unread post by HandaramTheGreat » Thu Dec 30, 2010 1:20 pm

btw, first one is $22^{10}+10P4\cdot22^6$
at most once=words without a,v,i,k + words which have a,v,i,k only once...
counting for second term:: taking 4 places from 10, they can be arranged in 10P4 ways... then other 6 places can be filled with other letters in $22^6$ ways...

i was really confused 'bout it...

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Moon
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Re: digit problem

Unread post by Moon » Sun Jan 02, 2011 3:28 am

Interesting...problem related to digits seem to be the most popular ones in this forum. :)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.

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