Question

In how many ways can the letters of the word 'fraction be arranged so that no two vowels are together?​

Answer 1

Answer:

14,400

Step-by-step explanation:

Given  

In how many ways can the letters of the word 'fraction be arranged so that no two vowels are together?

Fraction consists of 8 letters which has 3 vowels (a, I, o) and rest 5 are consonants.

Now arrange the consonants in 5! Ways = 120 ways

It can be -F- R- C- T- N so that no 2 vowels are together.

Now 3 vowels can fill these 6 places in (6,3) ways.

So total number of words will be  

120 x (6,3)

120 x 6 x 5 x 4

= 120 x 120

= 14,400