In how many ways can 5 girls be seated in a row so that two girls Ridhi and Sanya are:
(a) always together (b) never together
(b)Â there is no restriction as to the number of prizes that a boy may get.
(c) no boy sets all prizes.
(a) n = 6, r = 3
Number of permutations =Â
Hence, the number of ways, in which the three prizes can be awarded = 120.
(b) n = 6, Â r = 3
Number of permutations =Â
Hence, the number of ways in which 3 prizes can be awarded = 216.
(c) Number of ways in which one boy gets all prizes = number of boys = n = 6.
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There are 8 students appearing for an examination, of which 3 appear in mathematics paper, and 5 in other different subjects. In how many ways can they be seated if
(a)Â all the students appearing for mathematics paper are together.
(b)Â the students appearing for mathematics paper are not all together.
(c)Â no two students appearing in mathematics paper are seated together ?