Question

Anagrams are made by using the letters of the word ${}^{\prime }HINDUSTA{N}^{\prime }$ In how many of these anagrams do the vowels and consonants occupy the same relative positions as in ${}^{\prime }HINDUSTA{N}^{\prime }$

Answer 1

$HINDUSTAN$

Vowels and consonants occupy relative positions

Number of ways of arranging

(a) vowels $=(3$ blanks , $3$ vowels )

${=}^3{P}_3=3!$

$=6$ ways

(b) Consonants $=(6$blanks , $6$ letters $2$ same )

$=\frac{6!}{2!}$

Total Possiblities

$=\frac{6!}{2!}\times 6=2160$