Number of words which begins with a vowel and ends with a consonant by permuting the letters of the word $^{'} H A R S H I T A^{'}$

2340

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2700

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1800

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1980

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Solution

The correct option is C $2700$
Given word 'HARSHITA'
consonants (H,H), R,S,T vowels $\to$ (A,A),I
Total number of words starts with a vowel $= \frac{7}{2} + \frac{7}{2.2} = 3780$
Number of words starts and ends with a vowel (make two cases AA and IA)
$= \frac{6}{2} + 6 = 1080$
$∴$ number of words starts with a vowel and ends with a consonant = $3780 - 1080 = 2700$

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Number of words which begins with a vowel and ends with a consonant by permuting the letters of the word ′HARSHITA′

Number of words which begins with a vowel and ends with a consonant by permuting the letters of the word $^{'} H A R S H I T A^{'}$