The number of permutations of the letters of the word INDIA taken three at a time must be:

The letters in the word INDIA are (A, D, I, I, N ) Required permutation = coefficient of x3  in 3! (1+x1!+x22!)(1+x1!)3                                            = coefficient of x3 in 3[{1+(1+x)2}(1+x)3]                                            = coefficient of x3 in 3{(1+x)3+(1+x)5}                                            =3(3C3+5C3)=3(1+10)=33