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Question
How many strings are there using the letters of the word INTERMEDIATE, if vowels are never together
Solution
Vowels are never together:
Total number of arrangements using all the 12 letters of the given word
= `(12!)/(2! xx 2! xx 3!)`
= `(1 xx 2 xx 3 xx 4 xx 5 xx 6 xx 7 xx 8 xx9 xx 10 xx 11 xx 12)/(1 xx 2 xx 1 xx 2 xx 1 xx 2 xx 3)`
= 5 × 6 x 7 × 8 × 9 × 10 × 11 × 1
= 19958400
Number of arrangements where all the vowels are together = 151200
Number of arrangements where all vowels are never together = Total number of arrangements – number of arrangements where the vowels are together
= 19958400 – 151200
= 19807200
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