# 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?

A. 242

B. 240

C. 251

D. 275

### Solution(By Examveda Team)

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.
Hence, the rank of the word LABOUR is,
5! + 5! + 2 = 120 + 120 + 2 = 242

Note: 5! = 5 × 4 × 3 × 2 × 1 = 120

This Question Belongs to Arithmetic Ability >> Permutation And Combination

1. 3 1 2 4 6 5 (RANKING)
L A B O U R (WORD)
2 0 0 0 1 0 (TRICK U SHOULD CONCLUDE WHAT IS HAPPENING,,,,i.e.for'L' it is no of ranks which r less
than rank of 'L')
X X X X X X
5! 4! 3! 2! 1! 0!
......................................
2 X 5!+1

2. Why a & b only can bigining words.
Why only 2 time factorial given.
Why only two modification do in lastly.

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