A) 72
B) 27
C) 36
D) 64
Correct Answer: A
Solution :
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 \[=6+30+20+12+4=72\]
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