4 thoughts on “CAT 15 Lead-up – 10

  1. Hi Sir,

    While finding the number of ways to paint a cube, why didn’t we consider a factor of 6 ways for selecting the first colour (red in the given example)?

    • We are assuming a cube freely floating in space (i.e. i can turn/twist it in any direction). So when unpainted, all the faces will be effectively identical. So since every colour has to appear once, I just arbitrarily chose a colour and a position for it and then decided where to place the other colours relative to it. You could have started with any colour, it would make no difference.

      regards
      J

  2. In the cube case,after painting first two opposite sides,the remaining four sides can be viewed as four places in a circle.So they can be arranged in 3! ways.So total no of ways is 5*3!=30 ways.

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