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Q.
The rank of the word ‘FLOWER’ is
Permutations and Combinations
Solution:
Write down the letters of the word as Step (I) $ F\,L\,O\,W\,E\,R $
Rank the letter
according to dictionary $2 \,3\, 4 \,6\, 1\, 5$ Step (II)
Number of small numbers to the right of the letters
$1\, 1 \,1\, 2\, 0\, 0$
(Smaller than $2$ in the right of $2$ is only one number i.e. $1$, likewise for others)
Now rank of letter according to dictionary, use factorials started by $0!$ from the right to left below the every letter.
Write down product of the numbers given in block for each set
$= 120 + 24 + 6 + 4 + 0 + 0 = 154$
Now to obtain the rank of word add $1$ to the sum of these product.
Hence, required rank $= 154 + 1 = 155$
So the rank of the word $FLOWER$ is $155$.
