Jonah makes a smoothie for breakfast every morning. Today, he wants to use 4 different fruits. In how many different orders can he add these fruits to his blender?
Question
Jonah makes a smoothie for breakfast every morning. Today, he wants to use 4 different fruits. In how many different orders can he add these fruits to his blender?
Solution
This is a permutation problem. Permutations refer to the arrangement of items in a specific order.
The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items, r is the number of items to choose, and "!" denotes a factorial, meaning the product of all positive integers up to that number.
In this case, Jonah has 4 different fruits and he wants to know in how many different orders he can add these fruits to his blender. So, n = 4 (the total number of fruits) and r = 4 (the number of fruits he is choosing to add to the blender).
Using the formula, the calculation would be:
4P4 = 4! / (4 - 4)!
= 4! / 0!
= (4 * 3 * 2 * 1) / 1 (because 0! is defined to be 1)
= 24
So, Jonah can add the 4 different fruits to his blender in 24 different orders.
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