(i) There are 5 distinct letters in the word DIVYA.
∴ Number of permutations of the letters of the word DIVYA = 5! = 120
(ii) There are 9 letters in the word SHANTARAM in which ‘A’ is repeated 3 times.
∴ Number of permutations of the letters of the word SHANTARAM = \(\frac{9!}{3!}\)
= 9 x 8 x 7 x 6 x 5 x 4
= 60480
(iii) There are 9 letters in the word REPRESENT in which ‘E’ is repeated 3 times and ‘R’ is repeated 2 times.
∴ Number of permutations of the letters of the word REPRESENT = \(\frac{9!}{3!2!}\)
= \(\frac{9\times8\times7\times6\times5\times4}2\) = 30240
(iv) There are 7 distinct letters in the word COMBINE.
∴ Number of permutations of the letters of the word COMBINE = 7! = 5040
(v) There are 10 letters in the word BALBHARATI in which ‘B’ is repeated 2 times and ‘A’ is repeated 3 times.
∴ Number of permutations of the letters of the word BALBHARATI = \(\frac{10!}{2!3!}\)
\(=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{2\times3\times2}\)
= 302400
