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Question
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY
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Solution
The given word is FUNNY
To find the rank of the word FUNNY
Write down the letters of the word FUNNY.
Other than F in alphabetical order N, N, U, Y
Number of words beginning with F = `(4!)/(2!)`
= `(1 xx 2 xx 3 xx 4)/(1 xx 2)`
= 12 words
Among these words, the number of words beginning with FN = 3!
= 1 × 2 × 3
= 6 words
(Treating FN as one unit, the remaining 3 letters can be arranged in 3! ways)
The number of words beginning with FU is = `(3!)/(2!)`
= `(1 xx 2 xx 3)/(1 xx 2)`
= 3 words
Among these three words
FUNNY is the first word
Hence among the twelve words beginning with F
FUNNY appears as the 7th word.
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