The Wonderful Wizard of Math

Discrete Mathematics Level pending

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?

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