Question

(i) Find the number of different words by using all the letters of the word, ‘INSTITUTION’.

In how many of them 

(ii) are the three T’ s together

(iii) are the first two letters the two N’ s?

Answer 1

(i) There are 11 letters of which 3 are of 1 kind, 2 are of the 2^nd kind ,3 are of the 3^rd kind

Number of arrangements = \(\frac{11!}{3!2!3!}\) =554400 

(ii) Let all the three T’s be denoted by a single letter Z 

New word is INSIUIONZ 

Number of permutations = \(\frac{9!}{3!2!}\) = 30240

(iii) 

There are 9 places to be filled by 9 letters of which 3 are of 2 different kinds 

Number of permutations = \(\frac{9!}{3!3!}\) = 10080