how many ways can the word VENUS be arranged so that the vowels do not change thein orders??
1057lets assume cases here:
1)E _ _ _ _
in dis case other four can be arranged in 4!=24 ways..
2)_ E _ _ _
in dis case the first letter has 3 options(cant be U),3rd letter has 3 options,4th has 2 options nd de last 1ne has 1 option
total no of ways=3*3*2*1=18 ways
3) _ _ E _ _
in dis case de first letter has 3 options nd 2nd and 4th letter has 2 options nd de last 1ne has 1 option
no of ways = 3*2*2*1=12
4)_ _ _ E _
in dis case de last letter has to be u nd first three can be arranged in 3! ways.....=6 ways....
the last letter cant be E
total ways=24+18+12+6=60
actually another gud way of thinking dis is either de order will be E before U or E after U
so total ways will be 5!2 for each case....
1replace all vowels by x ..
so new word is
VxNxS
no.of ways of permutation is 5!2!
1to mantain the correct order "u" must come after "e"
So when e in frst place the rest can re arrange in 4! ways.
when in 2nd place frst place can be filld in 3 ways nd in each case d rest can re arrange in 3! ways. i.e 3*3!=18 ways..
similarly when in nxt place they cn arrange in 3p2 i.e 3! ways multiplied by 2 ways i.e 12 ways.
similarly in nxt case they ca rearrange in 3! ways
total no of ways =24+18+12+6= 60 ways
