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 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?
Number of letters in word 'ALLAHABAD' = (A → 4, L → 2, H → 1, B → 1, D → 1) = 9
Number of arrangements = 
(a) There are only four A's as vowels.
They can occupy even places (2, 4, 6, 8) in 
ways
∴ Number of ways in which vowels occupying even places = 1
We are left with 5 places and letters (L → 2, H → 1, B → 1, D → 1).
Number of permutations = 
Hence, total number of arrangements in which A's occupy even places
= 1 x 60 = 60.
(b) We first find the number of arrangements in which two L's are not together:
Number of arrangements in which two L's are together
Hence, the number of arrangements in which the two L's are not together
= (Total arrangements) - (the number of arrangements in which the two L's are together)
= 7560 - 1680 = 5880.
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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