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# If the letters of the word PRINCE are rearranged in all

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If the letters of the word PRINCE are rearranged in all [#permalink]

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04 Sep 2005, 09:46
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If the letters of the word PRINCE are rearranged in all possible ways to to form a 6 letter words without any of letter repeating and these wortds are in ascending order as in a dictionnary then what is the rank of the word prince in the list

plz explains yours works

thanks
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Re: PS arrangements tricky one [#permalink]

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04 Sep 2005, 13:53
mandy wrote:
Hello

If the letters of the word PRINCE are rearranged in all possible ways to to form a 6 letter words without any of letter repeating and these wortds are in ascending order as in a dictionnary then what is the rank of the word prince in the list

plz explains yours works

thanks

P R I N C E
5 6 3 4 1 2

there are 5 choices for the left most digit, all the way to right most digit
(with 2 choices). So that will be 5x6x3x4x1x2 = 720

Does that sound right ?
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04 Sep 2005, 18:27
every letter has its ranking

P-5
R-6
I-3
N-4
C-1
E-2

Let's count the number of arrangemenst for # 1 thru 4:

!5X4=360

Now we have to count the # of arrangements whaen the first letter is P:
For #1,2,3,4 there are:

4!X4=96 arrangements

Now we have to count how many arrangements for #1, and #2 for the PR_ _ _ _ exist:
!3X2=12

Now we have to count how many arrangements for #1, and #2 for the PRI _ _ _ exist:

!2X2=4

Add all this mess together:

360+96+12+4= 472
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25 Sep 2005, 16:40
C E I N P R

C, E, I, N - 4*5! = 480

P - C, E, I, N - 4*4! = 96

PR - C, E = 2*3! = 12

PRI - C, E = 2 * 2! = 4

PRINCE

480 + 96 + 12 + 4 = 592
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25 Sep 2005, 18:12
not easy, quite long...

I found 593, so close to dil66's 592

total ways : 6! = 720

It is in alphabetical order so the best way is to do : 720 - excluded

To know what possibilities will be exluded :

1) All possibilities begining by R (120 possibilities)
2) we have to stoip after PRINCE and I've already excluded all words begining with R, so P is the first letter, then R is the least possible so there will be no other words after with another letter here (R is the lowest one here considering the alphabetical order), then we have I who is not the lovest one so we an have words with I and N.
words with I (but behind PRINCE in alphabetical order) : PRINEC = 1 word
words with letter N instead of I : 1*1*1*3*2= 6 words

Total Excluded : 120+6+1=127
Rank of the word PRINCE : 720-127=593
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27 Sep 2005, 05:44
I agree with antmavel's solution. 593.

Suslik, your reasoning is correct but: 4*5! = 480, and you also forgot to add 1 to your result. You have calculated the number of words before prince, you still need to add 1.
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27 Sep 2005, 17:44
Can someone explain the question in more detail...

I didnt understand what the question asks for..
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28 Sep 2005, 01:53
The question asks you to take the word prince and arrange its letters in all possible ways. You obtain 6! words (does not matter if they are not real words).

Then, you have to take those 6! words and list them like in a dictionary.

1 ceinpr
2 ceinrp
....

593 prince

I hope this helps....
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Re: PS arrangements tricky one [#permalink]

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30 Sep 2005, 02:37
@Antmavel - your solution was excellent. Thank you.

Sreeni
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Re: If the letters of the word PRINCE are rearranged in all [#permalink]

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14 Jan 2012, 02:50
let's see how many are below PRINCE.

R*5! = 120
PRN*3! = 6
PRINEC = 1
total = 127

rank = 6! - 127 = 593
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Re: If the letters of the word PRINCE are rearranged in all   [#permalink] 14 Jan 2012, 02:50
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# If the letters of the word PRINCE are rearranged in all

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