1.

In how many differents ways can the letter of the word 'professional'be arranged in such a way that the vowels always come together?

Answer»

Total NUMBER of vowels- o,e,i,o,a = 5 ( 1 REPEAT)

professional contains 12 letters it can be GROUPED as p,r,f,s,s,n,l, (o,e,I,o,a) as 8 units. vowels are considered as 1 unit here

To arrange these 8 units total possible ways= 8!/2! (as s repeats 2 times)

And the vowels can be arranged among themselves in 5!/2! ways ( o repeats Twice)


so total no of ways is 8!*5!/4 = 12,09,600


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