the solution of a problem is this:Total number of words = 5! = 120!If all thevowels come together, then we have: (O.E.A.), M,GThese canbe arranged in 3! ways.But (O,E.A.)can be arranged themselves in 3! ways.=> Numberof ways, when vowels come-together = 3! x 3!= 36 ways=> Number ofways, when vowels being never-together=120-36 = 84 ways.but why not,like this:-O X E XAover 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.

Anmol Nanda , 14 Years ago

Grade 11