The Wonderful Wizard of Math

Probability Level 3

There are 100 people in the school play. There are 5 trees, 5 munchkins, 10 dwarfs, 5 bushes, 5 peasants, 50 villagers, 10 cards, and 10 lords. The trees, bushes, and munchkins have to stand on a line. The peasants stay in line as well, but they have a pre-made order that cannot be changed. The villagers have to line up from youngest to oldest, and there are only two people there who have the same age, and can switch places. Each of the lords picks a random card and stands next to it. How many different ways can all the people line up?


The answer is 12541132800000.

John Newman by John Newman , 24, USA

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1 solution

Charlz Charlizard
Dec 29, 2019

So here we can clearly see that the arrangement will be:

  • 5 tress can be arranged that is 5! = 120
  • 5 munchkins can be arranged in 5! = 120
  • 5 bushes can be arranged in 5! = 120
  • Villagers can be arranged in only 2 positions
  • 10 dwarfs can be arranged in 10! = 3628800
  • And the lords and the cards can be arranged in 1 way as they have already selected their card.

So total arrangement= 120 * 120 * 120 * 3628800 * 2 = 12541132800000

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