If the letters of the word PRINCE are rearranged in all

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.

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 ?

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

Can someone explain the question in more detail...

I didnt understand what the question asks for..

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....

@Antmavel - your solution was excellent. Thank you.

Sreeni

let's see how many are below PRINCE.

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

rank = 6! - 127 = 593

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.