We are to form different words with the letters of the word ‘INTEGER’. Let 
be the number of words in which I and N are never together, and 
be the number of words which begin with I and end with R . Then 
is equal to
Text Solution
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We have 5 letters other than ‘ I ’ and ‘ N ’ of which two are identical ( E ' s ). We can arrange these letters in a line in 
ways. In any such arrangement ‘ I ’ and ‘ N ’ can be placed in 6 available gaps in 
ways, so required number = 
.
Now, if word start with I and end with R then the remaining letters are 5. So, total number of ways = 
.
.`
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