Total number of ways of selecting five letters from letters of the word INDEPENDENT is

There are 11 letters in the given word which are as follows (NNN) (EEE) (DD)IPT 

Five letters can be selected in the following manners :

(i) All letters different: ${ }^6{\mathrm{C}}_5=6$

(ii) Two similar and three different ${:}^3{\mathrm{C}}_1{\cdot }^5{\mathrm{C}}_3=30$

(iii) Three similar and two different ${:}^2{\mathrm{C}}_1{\cdot }^5{\mathrm{C}}_2=20$

(iv) Three similar and two similar ${:}^2{\mathrm{C}}_1{\cdot }^2{\mathrm{C}}_1=4$

(v) Two similar, two similar and one different : ${ }^3{\mathrm{C}}_2{\cdot }^4{\mathrm{C}}_1=12$

$\therefore$ Total selections $=6+30+20+4+12=72$