I need to permute letters of 'CINEMA'. I need to maintain the order of I,E,A but they need not be together

Question

The letters I,E & A have to be situated in that order only. But they need not be together. valid permutations are for eg: IENCMA, CIENAM etc. IN how many ways can the letters of CINEMA be arranged linearly?? Pls Help!!

Answer 1

Okay, IEA_ _ _ , IE_A_ _, IE_ _A_ , IE_ _ _A, I_EA_ _, I_E_A_ and so on are (6 choose 3)=20 combinations.You cant have permutations if you want them to be in I-E-A order only. So each of the above will have 3!=6 combinations of CNM( CMN, MCN, MNC, CNM, CMN). Hence total combinations will be 20x3!=20x6=120 combinations.

Answer 2

dilema, vietnam, like that?