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Discrete Mathematics

# Permutations Without Repetition

How many different ways can you stack a scoop of chocolate ice cream, a scoop of pistachio ice cream, a scoop of vanilla ice cream, and a scoop of strawberry ice cream onto an ice cream cone?

Six friends Andy, Bandy, Candy, Dandy, Endy and Fandy want to form a club. They decide that there will be 1 president, 1 secretary and 4 ordinary members. How many different ways can they organize this club?

6 friends (Andy, Bandy, Candy, Dandy, Endy and Fandy) are out to dinner. They will be seated in a circular table (with 6 seats). How many ways are there to seat them?

Details and assumptions:
If two seating arrangements are rotations of each other, they're considered the same. If two seating arrangements are reflections of each other, they're considered different.

Five children--Myra, Esmond, Yolanda, Carlos, Lin--are playing a game of hide-and-go-seek. Myra counts to 100 and the other four children each go to hide in one of the rooms of the house. If there are $$7$$ rooms that the children could hide in, and each hides in a different room, how many different ways can the children hide?

On a trip to the local zoo, there are $$6$$ exhibits that you want to visit. In how many different orders can you visit the exhibits?

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