Q. 273.9( 8 Votes )

Find the number o

Answer :

There are 3N,4E,2D,1l,1P,1C


Since letters are repeating so we use the formula .


Total number of arrangements are:



= 1663200


(i) If word starts with P.



Now P will be fixed,


We now need to arrange 11 letters.


Where there are 4E,3N,2D


Since letters are repeating so we use the formula .


No. of arrangements


= 138600


(ii) do all the vowels always occur together


We will consider vowels as a same letter. Here there are 5vowels i.e IEEEE,


So, these can be arranged in ways as E is repeating 4 times.


Now total letters are 7+1 = 8


Now there are 3N,2D in remaining letters.


These can be arranged in ways.


Total ways


= 16800


iii) do all the vowels never occur together


Vowels never occur together = Total arrangements – vowels occur together


= 1663200 – 16800


= 1646400


iv) do the words begin with I and end in P?


Let’s fix I and P at the ends.



There are 2D,4E,3N.


As letters are repeating,


Total arrangements


= 12600


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