Let n be the number of ways in which the letters of the word "RESONANCE" can be arranged so that vowels appear at the even places and m be the number of ways in which "RESONANCE" can be arrange so that letters R, S, O, A, appear in the order same as in the word RESONANCE, then answer the following questions.
(i) The value of n is
Text Solution
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(i) In the word RESONANCE there are 9 letters.
Consonants (5), 1R, 1S, 1C and 2N
Vowels (4), 2E, 1O, 1A
total even places 4 ;
No. of ways arranging vowels in even places is 
= 12
No. of ways arranging consonants in remaining odd places is 
= 60
required number of arrangement = 12 × 60 = 720 = n
(ii) Required number of arrangements are 
= 3780
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