Short Answer TypeNumber of letters:
A → 3, S → 4
I → 2, N → 2
T → 1, O → 1
Total letters 13.
Tie the four S's.
Number of arrangements = 
...(i)
Mix with remaining to give:
[3 (A) + 2 (I) + 2 (N) + 1 (T) + 1 (O)] + 1 = 10
Fix O at first place.
Number of permutations = 
...(ii)
Fix T at the last place.
Number of permutations = 
...(iii)
Now, we have
3 (A) + 2 (I) + 2 (N) + 1 (four S's tied) = 8 letters
Number of arrangements = 
Hence, by fundamental principle of counting, the total number of permutations
= 1 x 1 x 1 x 1680 = 1680.
Long Answer TypeHow many different words, with or without meaning can be formed, by using the letters of the word ‘HARYANA’? Also, find as to:
(a) how many of these begin with H and end with N?
(b) in how many of these H and N are together?
Short Answer TypeLong Answer TypeHow many different words can be formed by using the letters of the word ‘ALLAHABAD?
(a) In how many of these do the vowels occupy even positions.
(b) In how many of these, the two L’s do not come together?
Short Answer TypeFind the number of permutations of 6 students sitting around a round table.
(a) In how many of these arrangements are three of the students sit together ?
(b) In how many of the arrangements, three of the students do not sit all together ?
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