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?
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 ?
Number of arrangements for 6 students to sit around a round table = (6 - 1)! = 5! = 120.
(a) Tie the three students.
Number of arrangements = 
Mix with the remaining to give a toal of 3 + 1 = 4
Seat them around a round table.
∴ The number of permutations = (4 - 1)! = 3! = 6.
Hence, the number of arrangements in which the 3 students sit together = 6 x 6 = 36
[By using (i) and (ii)]
(b) The number of arrangements in which the 3 students do not sit all together = 120 - 26 = 84.
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