Question

find the number of permutation of letters of the word EXERCISE in which vowels are together​

Answer 1

Answer:

Question:

Find the permutation of letters of the word EXERCISES in which vowels are together.

My Efforts:

I have rearranged the word in such a way that all the vowel come together.

EEEI XRCSS

Now the vowels can be arranged in 4!3!(E is repeated 3 times) ways and remaining letters can be arranged in 4!2!(S is repeated 2 times) ways.

Further above shown arrangement can be permuted in 2! ways(Consonant can be written first and then vowel.)

So total permutation possible

4!3!×4!2!×2!=96

But the answer given is 1440 is is far more than mine, I am surely missing something.