Question

Find the number of different words that can be formed from the letters of the word intermediate such that 2 vowels never come together

Answer 1

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Answer 2

Answer:

Total number of consonants =6

Total number of vowels =6

Total number of letters in the word INTERMEDIATE =12

Number of ways of arranging the consonants of which two are alike =6!/2!  = (6*5*4*3*2)/2*1  = 360

Number of ways of arranging the vowels =⁷P₆*1/3!*1/2!  = 7!/1!*1/3!*1/2!  = (7*6*5*4*3!)/ (3!*2)  = 420

Total number of ways =420*360  = 151200