Short Answer TypeNumber of letters in word 'ORIENTAL' = 8 (all distinct)
Number of letters to be used = 8
Step I: Â Â Â A and E are to occupy odd places marked X
            Number of letters = 2 (A and E)
            Number of boxes = 4
   
               n = 4, r = 2
   Number of permutations of arranging A and E = 
 ...(i)
Step II:Â After A and E are fixed, there will be 6 letters left and 6 boxes for them.
       (A and E use up two boxes)
       
 Number of permutations of arrranging the remaining letters =
 ...(ii)
       Hence, from (i) and (ii), the total number of words formed = 12 x 720 = 8640.
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
Long Answer Type(b)Â there is no restriction as to the number of prizes that a boy may get.
(c) no boy sets all prizes.
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 ?
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