It is currently 12 Dec 2017, 05:24

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If the letters of the word PRINCE are rearranged in all

Author Message
TAGS:

Hide Tags

Senior Manager
Joined: 30 May 2005
Posts: 274

Kudos [?]: 45 [0], given: 0

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

Show Tags

04 Sep 2005, 09:46
00:00

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 100% (04:18) wrong based on 1 sessions

HideShow timer Statistics

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

Kudos [?]: 45 [0], given: 0

Senior Manager
Joined: 04 May 2005
Posts: 278

Kudos [?]: 88 [0], given: 0

Location: CA, USA
Re: PS arrangements tricky one [#permalink]

Show Tags

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 ?

Kudos [?]: 88 [0], given: 0

Intern
Joined: 24 Aug 2005
Posts: 8

Kudos [?]: [0], given: 0

Show Tags

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

360+96+12+4= 472

Kudos [?]: [0], given: 0

Intern
Joined: 25 Jun 2005
Posts: 23

Kudos [?]: 1 [0], given: 0

Location: Bay Area, CA

Show Tags

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
_________________

If you can't change the people, change the people.

Kudos [?]: 1 [0], given: 0

VP
Joined: 13 Jun 2004
Posts: 1111

Kudos [?]: 52 [0], given: 0

Location: London, UK
Schools: Tuck'08

Show Tags

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

Kudos [?]: 52 [0], given: 0

Manager
Joined: 03 Aug 2005
Posts: 134

Kudos [?]: 4 [0], given: 0

Show Tags

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.

Kudos [?]: 4 [0], given: 0

Intern
Joined: 27 Aug 2005
Posts: 33

Kudos [?]: 2 [0], given: 0

Show Tags

27 Sep 2005, 17:44
Can someone explain the question in more detail...

I didnt understand what the question asks for..

Kudos [?]: 2 [0], given: 0

Manager
Joined: 03 Aug 2005
Posts: 134

Kudos [?]: 4 [0], given: 0

Show Tags

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....

Kudos [?]: 4 [0], given: 0

Senior Manager
Joined: 15 Apr 2005
Posts: 414

Kudos [?]: 18 [0], given: 0

Location: India, Chennai
Re: PS arrangements tricky one [#permalink]

Show Tags

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

Sreeni

Kudos [?]: 18 [0], given: 0

Senior Manager
Status: mba here i come!
Joined: 07 Aug 2011
Posts: 261

Kudos [?]: 1259 [0], given: 48

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

Show Tags

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
_________________

press +1 Kudos to appreciate posts

Kudos [?]: 1259 [0], given: 48

Re: If the letters of the word PRINCE are rearranged in all   [#permalink] 14 Jan 2012, 02:50
Display posts from previous: Sort by