Trudy and her friends are making dessert at a sleepover. They need to add 8 ingredients to a bowl. In how many different orders can they add these ingredients?
Question
Trudy and her friends are making dessert at a sleepover. They need to add 8 ingredients to a bowl. In how many different orders can they add these ingredients?
Solution
This is a permutation problem. The number of ways to arrange n distinct objects in a row is given by n factorial (n!).
Step 1: Identify the number of distinct objects. In this case, the distinct objects are the 8 ingredients.
Step 2: Calculate the factorial of the number of distinct objects. The factorial of a number n is the product of all positive integers less than or equal to n.
So, the number of different orders in which they can add these ingredients is 8! (8 factorial), which is 8765432*1 = 40,320.
Therefore, Trudy and her friends can add the 8 ingredients in 40,320 different orders.
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