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Question

Column - 1 and 2 consist of different words, number of selection of 3 letters from the word respectively.

Column-IColumn-II(I)DREAM(P)70(II)DEDICATION(Q)10(III)POWERFUL(R)77(IV)COMBINATION(S)56

Which of the following is the only CORRECT combination?

A
(I)(P)
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B
(II)(Q)
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C
(III)(S)
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D
(IV)(Q)
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Solution

The correct option is C (III)(S)
Number of ways 3 letters can be selected from thegiven words is as follows:
DREAM –––––––––3 letters can be selected out of 5 different lettersin number of ways=5C3=10
DEDICATION ––––––––––––––––There can be two cases possible.All distinct letters can be selected in 8C3 ways.1 pair and 1 distinct can be selected in2C1×7C1 waysTotal number of ways=2C1×7C1+8C3=70
POWERFUL–––––––––––––3 letters can be selected out of 8 different lettersin number of ways=8C3=56
COMBINATION–––––––––––––––––There can be two cases possible.All distinct letters can be selected in 8C3 ways.1 pair and 1 distinct can be selected in3C1×7C1 waysTotal number of ways=3C1×7C1+8C3=77



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