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Question

Find the total numbers of ways of selecting 5 letters from the following of word INDEPENDENT .

A
36
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B
48
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C
72
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D
84
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Solution

The correct option is C 72
word INDEPENDENT has 2Ds,3Es,3Ns and I,P,T
Hence the 5 numbers can be selected as follows:
3 alike ,2 different =(21)×(52)=20
3 alike ,2 other alike=(21)×(21)=4
2 alike ,3 different=(31)×(53)=30
2 alike ,2 other alike and 1 different=(32)×(41)=12
All different =(65)=6
Therefore, total no. of ways of selection =(20+4+30+12+6)=72

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