Judith makes a smoothie for breakfast every morning. Today, she wants to use plum, orange, peach, apricot, pineapple, and apple. In how many different orders can she add these fruits to her blender?
Question
Judith makes a smoothie for breakfast every morning. Today, she wants to use plum, orange, peach, apricot, pineapple, and apple. In how many different orders can she add these fruits to her blender?
Solution
This is a permutation problem. Permutations refer to the arrangement of items in a specific order. When the order of items matters, we use permutations.
In this case, Judith has 6 different fruits and she wants to know in how many different orders she can add these fruits to her blender.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of items,
- r is the number of items to choose,
- "!" denotes factorial, which means multiplying all positive integers up to that number.
In this case, n = 6 (plum, orange, peach, apricot, pineapple, and apple) and r = 6 (since she is using all the fruits).
So, the calculation becomes:
P(6, 6) = 6! / (6-6)!
= 6! / 0!
Note: By definition, 0! is equal to 1.
So, P(6, 6) = 6! / 1
= 6 x 5 x 4 x 3 x 2 x 1
= 720
Therefore, Judith can add the fruits to her blender in 720 different orders.
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