find the rank of the word:IITJEE
Answers
Answer:
They are I, I, T, J, E , E. Arranging these letters according to the English alphabet,we get E,E,I,I,J,T.
Case 1: All E letter words
E_ _ _ _ _ . The total permutations of letters in the five blank spaces =5!/2! (I have divided by 2! since there are two I’s in the remaining group of letters.
5!/2!=60
Thus, the first 60 words are E letter words
Case 2: All I letter words
Since the word we are searching for is also an I letter word(IITJEE), we will have to restrict it further
So now we consider all words starting with IE
IE_ _ _ _.The total permutations of letters in the four blank spaces =4!=24
Thus,the next 24 words are starting with IE
Going further ,
Consider words starting with II now.Again,the word we are searching for also starts with II, we will have to restrict further
(i) I I E _ _ _ .Total permutations=3!=6
(ii)I I J_ _ _.Total permutations=3!/2!=3 (I have divided by 2! because there are two E’s repeated)
(iii)I I T _ _ _. The three blanks can be filled by EEJ,EJE or JEE. JEE is the required arrangement which is 3rd according to the three arrangements EEJ , EJE< JEE (Alphabetically speaking)
Therefore the rank=60+24+6+3+3=96th rank
yes we can do it so by permutations and combinations.....
soln is 96
