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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.
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.
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.
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.
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