IIT JEE , AIEEE Forum - Mathematics , Algebra - How many different words can be formed with the letters of the word ?PATLIPUTRA? without c

spideyunlimited

According to ur question... vowels can only interchange places with vowels, and consonants can only interchange places with consonants .....

Consider Consonants ----

6! / 2! 2!

6! because there are 6 letters excluding the vowels.
2! because T is repeated twice
another 2! because P is repeated twice

Now consider vowels ----

4! / 2!

4 vowels, and A repeated 2 times

So total number of words that can be formed are :

= (6! / 2! 2!). (4! / 2!)

= 6! . 3

= 2160 words

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