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Summer Maths Puzzles - Friday 23 August - Pot Luck Pet Prizes

Pot Luck Pet Prizes

Lady Luck is about to give out the prize envelopes following the Pet Show at the Annual Village Fete.

  • In the Tortoise Class, 1 of the 3 tortoises was awarded Highly Commended and the others were awarded Commended.
  • In the Cat Class, 2 of the 4 cats were awarded Highly Commended and the others were awarded Commended.
  • And in the Dog Class, 3 of the 5 dogs were awarded Highly Commended and the others were awarded Commended.

Unfortunately, the prize envelopes have been muddled up. Lady Luck decides to go ahead and select envelopes at random (fortunately she knows that the yellow envelopes are for the tortoises, the green envelopes are for the cats, and the blue envelopes are for the dogs).

What is the probability that everyone gets the right prize?

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons