A fairly easy one.. 1. In how many ways can the word

A fairly easy one..

1. In how many ways can the word CONSTANTINOPLE be arranged?
2. In how many ways can the above word be arranged with vowels and consonants taken together?
3. In how many ways can the word be arranged such that no two vowels are together?
4. Also find probability of having NO two consonants together?

the answere for the first one is :

14! / (3!*2!*2!)


Ans 2:

if i interpret u question that consonants taken "appearing togeather " and vowels "appearing togeather"..then we have 5 vowels out of which 2 are same therefore number of ways we can arrange these togeather is ( 5!/2!)

take this as one unit and then arrange it with the consonants which are 9 with 3 and 2 being the same....

so total number of ways u can arrange both sets is

10! / 3!2! multiplied by 5!/2!

10! 5! / 3! 2! 2!..

Ans 3 :

No two vowels are togeather means ..... there are 10 spaces between the 9 consonants...

to make sure that no two vowels are togeather means that vowels needs to be arranged within these 10 spaces ....
10*9*8*7*6 / 2!

and rest of the 9 consonants can be arranged separately 9!/3!2!

10C5 *9! / 3!2!2!



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