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```        the solution of a problem is this:
Total number of words   =   5!   =    120!
If all the  vowels come together, then we have: (O.E.A.), M,G
These can  be arranged in    3!    ways.
But (O,E.A.)  can be arranged themselves in   3! ways.
=> Number  of ways, when vowels come-together  =    3!  x    3!
= 36 ways
=> Number of  ways, when vowels being never-together
=  120-36        =  84 ways.
but why not,
like this:-
O  X  E X   A
over here the position of X can be filled by 2! ways and OEA in 3! ways,what more selections am i missing?
becoz total ways according to my analysis is 12 but according to this process is 84.

```
6 years ago

jishnu prakash
15 Points
```										Consider the cases in which two vowels are at one place and the third vowel away from them for example
o e m g a
a g m o e
the solution includes these too.

```
6 years ago
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