Find the number of words formed by permuting all letters of the word INDIA. In how many of them have vowels together ?

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Solution

Number of letters in the word INDIA = 5
Number of same letters in the word INDIA = 2
Thus, Number of words formed by permuting all the letters of the word $= \frac{5!}{2!} = 5 \times 4 \times 3 = 60$
No. of words in which vowels are together $= 3! \times \frac{3!}{2!} = 18$

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Find the number of words formed by permuting all letters of the word INDIA. In how many of them have vowels together ?

Number of letters in the word INDIA = 5Number of same letters in the word INDIA = 2Thus, Number of words formed by permuting all the letters of the word =5!2!=5×4×3=60No. of words in which vowels are together=3!×3!2!=18

Number of letters in the word INDIA = 5
Number of same letters in the word INDIA = 2
Thus, Number of words formed by permuting all the letters of the word $= \frac{5!}{2!} = 5 \times 4 \times 3 = 60$
No. of words in which vowels are together $= 3! \times \frac{3!}{2!} = 18$