Short Answer Type
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 TypeNumbers of letters in 'RANDOM' = (R → 1, A → 1, N → 1, D → 1, O → 1, M → 1) = 6
Number of words that begin with A = 
Number of words that begin with D = 
Number of words that begin with M = 
Number of words that begin with O = 
Number of words that begin with N = 
So far, we have formed 120 + 120 + 120 + 120 + 120 = 600 words.
Now words starting with R.
Number of words starting with RAD = 1 x 1 x 1 x 3! = 6.
Number of words starting with RAM = 1 x 1 x 1 x 3! = 6.
Total words = 600 + 12 = 612.
613th word is RANDMO
614th word is RANDOM
∴ Rank of the word random in a dictionary is 614.
Long 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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