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Question 9 : How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

  1. 1988
  2. 1976
  3. 1966
  4. 1956

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Explanatory Answer

Let the 6 colors be Violet, Indigo, Blue, Green, Yellow, Orange
Among this, any 1 can be selected from 6 = 6C1 ways = 6 ways

When selecting 2 - We can select (Violet and Indigo) and (Indigo and Violet) = 6P2 = 30
For 3 , 6P3 = 6 × 5 × 4 = 120 ways
For 4 , 6P4 = 6 × 5 × 4 × 3 = 360 ways
For 5 , 6P5 = 6 × 5 × 4 × 3 × 2 = 720 ways
For 6 , 6P6 = 6 × 5 × 4 × 3 × 2 × 1 = 720 ways Total 1956 ways.

The question is " How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time? "

Hence, the answer is 1956

Choice D is the correct answer.

 

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