If the letters of the word PRINCE are rearranged in all

Question

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

plz explains yours works

thanks

Antmavel · Accepted Answer

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

qpoo · Answer

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 ?

suslik · Answer

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

dil66 · Answer

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

jdtomatito · Answer

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.

nisha_qutu · Answer

Can someone explain the question in more detail... 

I didnt understand what the question asks for..

jdtomatito · Answer

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....

krisrini · Answer

@Antmavel - your solution was excellent. Thank you.

Sreeni

MBAhereIcome · Answer

let's see how many are below PRINCE.

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

rank = 6! - 127 = 593

srvkmr88 · Answer

Word P R I N C E

Alphabetical arrangement of the letters is C E I N P R

1.) Word starting with letter C _ _ _ _ _ can be done in 5! ways but its not our destination.

2.) Word starting with letter E _ _ _ _ _ can be done in 5! ways but its not our destination.

3.) Word starting with letter I _ _ _ _ _ can be done in 5! ways but its not our destination.

4.) Word starting with letter N _ _ _ _ _ can be done in 5! ways but its not our destination

5.) Word starting with letter "P", here we got our first letter. Next letter will be "C' as per dictionary arrangement.
 Word starting with P C _ _ _ _ can be done in 4! ways.
6.) Word starting with P E _ _ _ _ can be done in 4! ways.

7.) Word starting with P I _ _ _ _ can be done in 4! ways.

8.) Word starting with P N _ _ _ _ can be done in 4! ways.

9.) Word starting with "P R", here we got our first two letters. We will jump on to third letter
 P R C _ _ _, can be done in 3! ways. 
10.) P R E _ _ _, can be done in 3! ways.

11.) P R I, here we got 3 required letters. now for 4th letter.
 P R I C _ _ can be done in 2! ways.

12.) P R I E _ _ can be done in 2! ways.

13.) P R I N, here we got 4 required letter. Jumping on to 5th letter.
 P R I N C E, so at this step we have go all the required letters. So + 1 for this step

total = 5! x 4 + 4! x 4 + 3! x 2 + 2! x 2 + 1 = 593. Th word PRINCE will appear on 593rd position.

ThickGuitar · Answer

IMHO, This question is a time vampire and best way is to ballpark it and move on in less than a minute. The aim is to make an intuitive guess.

5! = 720/6 = 120 so each block (letter) has 120 words.
Arrange the word PRINCE in alpha-order = CEINPR.

All words starting with the letter P end at 600 ranking, and they start at 481. Since the letter right after P is R, which is bottom of the barrel, that means the word prince has to have a ranking very close to 600. Depending on the answers given, pick your best guess and keep it moving.

If the letters of the word PRINCE are rearranged in all

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If the letters of the word PRINCE are rearranged in all

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards