As head of Brilliant's cybersecurity, you need to know how many different passwords can be created by rearranging the digits 1, 2, 3, 4, 5, and 6. Can you count them all?
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?