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Tamil Nadu Board of Secondary EducationHSC Science Class 11

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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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

Sum
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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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Chapter 4: Combinatorics and Mathematical Induction - Exercise 4.2 [Page 178]

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Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 4 Combinatorics and Mathematical Induction
Exercise 4.2 | Q 18 | Page 178

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