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Anmol Nanda 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:-

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.


7 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.


7 years ago
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