Given a string ‘S’ containing vowels and consonants of lowercase English alphabets. The task is to find the number of ways in which the characters of the word can be arranged such that the vowels occupy only the odd positions.
First find the total no. of odd places and even places in the given word.
Total number of even places = floor(word length/2)
Total number of odd places = word length – total even places
Let’s consider the string “contribute” then there are 10 letters in the given word and there are 5 odd places, 5 even places, 4 vowels and 6 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Now, 4 vowels can be placed at any of the five places, marked 1, 3, 5, 7, 9.
The number of ways of arranging the vowels = 5_P_4 = 5! = 120
Also, the 6 consonants can be arranged at the remaining 6 positions.
Number of ways of these arrangements = 6_P_6 = 6! = 720.
Total number of ways = (120 x 720) = 86400
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Improved By : Mithun Kumar