We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2? Choose the correct choice from the following options.
A) 18
B) 24
C) 30
D) 36
E) 40
Total possible combination without any restriction:- 7!/2! (E is mentioned two times in the word INTEGER, hence we are dividing by 2!)   Total Possible combination when letter 'I' and 'N' are together- 6!*2/2! (Think of I and N as one, hence total letters are 6, but I and N can be written in two ways- IN and NI- that is why we multiplied 6!*2)   Total possible combination when letter 'I' and 'N' are not together, i.e. m1= 7!/2! - 6!*2/2!= 6!*5/2   Now fix 'I' and 'R', then total possible combination, i.e m2, are= 5!/2!   m1/m2= 6!*5/2/5!/2= 30   Answer is '30'
<result>C</result>
We are required to form different words with the help of letters of the word INTEGER. Let m1 be the number of words in which I and N are never together and m2 be the number of words which begin with I and end with R, then what is the value if m1/m2?