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Grade: 11

                        

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.

9 years ago

Answers : (1)

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.

 

9 years ago
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