How many different words can be formed from the letters of the word INTERMEDIATE? In how many of them, two vowels never come together?

Explanation

Total number of letters in the word 'INTERMEDIATE' = 12
out of which 6 are consonants and 6 are vowels. The arrangement of these 12 alphabets in which two vowels never come together can be understand with the help of follow manner.
`{:(V, C, V, C, V, C, V, C, V, C, V, C, V):}`
6 consonants out of which 2 are alike can be placed in `(6"!")/(2"!")` ways and 6 vowels, out of which 3 E's alike and 2 I's are alike can be arranged at seven place in `""^(7)P_(6) xx (1)/(3"!") xx (1)/(2"!")` ways.
`therefore` Total number of words `=(6"!")/(2"!") xx ""^(7)P_(6) xx (1)/(3"!") xx (1)/(2"!") = 151200`