problem gre combination 245

Question

The letter of the word LABOUR are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word LABOUR?

i don't know about right answer ,but it may be........ The order of each letter in the dictionary is ABLORU. Now, with A in the beginning, the remaining letters can be permuted in 5! ways. Similarly, with B in the beginning, the remaining letters can be permuted in 5! ways. With L in the beginning, the first word will be LABORU, the second will be LABOUR

Answer 1

The position of the word "LABOUR" is: $5! + 5! + 2 = 242$th

Answer 2

First, assign each letter with a relative weight by alphabetic order:

• $A=0$
• $B=1$
• $L=2$
• $O=3$
• $R=4$
• $U=5$

Then, multiply each letter's weight by the factorial of the letter's index in the word $LABOUR$:

• $L\rightarrow2\times5!$
• $A\rightarrow0\times4!$
• $B\rightarrow1\times3!$
• $O\rightarrow3\times2!$
• $U\rightarrow5\times1!$
• $R\rightarrow4\times0!$

Finally, sum up the results: $2\times120+0\times24+1\times6+3\times2+5\times1+4\times1=261$

Answer 3

We have to see how many words come before it. To do this for each letter you have to go letter by letter and calculate how many letters "smaller" than that letter are to the right of that letter.In LABOUR. The rank of the word is going to be the sum of the first number multiplied by 5! plus the sum of the second number multiplied by 4! and so on plus one.

L has 2 smaller letters to its right.

A has 0 smaller letters to its right.

B has 0 smaller letters to its right.

O has 0 smaller letters to its right.

U has 1 smaller letters to its right.

R has 0 smaller letters to its right

Therefore the rank of labour is $2(5!)+1(1!)+1=242$