Question

The total number of ways of selecting five letters from the letters of the word 'INDEPENDENT' is

• A. 72
• B. 27
• C. 36
• D. 64

Answer 1

Answer: (A)

Word 'INDEPENDENT' here, $1-1,N-3,D$ $2,E-3,P-1,T-1$
Selection can be made by the following number of ways
(i) If all the letters are distinct, then no. of ways
${=}^6{C}_5=6$
(ii) If three are different and two letters are same, then no. of way ${=}^3{C}_1{.}^5{C}_3=30$
(iii) If two letters are different and three are same, then ways
${=}^2{C}_1{.}^5{C}_2=20$
(iv) If two letters are same another two letters are same and one letter is different, then no. of ways
${=}^3{C}_2{.}^4{C}_1=12$
(v) If three letters are same and another two letters are same, then ways
${=}^2{C}_1{.}^2{C}_1=4$
$\therefore$ Total number of ways
$=6+30+20+12+4=72$