A store that sells 5 different types of candy bars would like to put a box of each type on a shelf at the checkout. However, there is only space for 3 boxes. How many arrangements of 3 different candy bar boxes are possible?
Question
A store that sells 5 different types of candy bars would like to put a box of each type on a shelf at the checkout. However, there is only space for 3 boxes. How many arrangements of 3 different candy bar boxes are possible?
Solution
This is a problem of combinations. The store has 5 different types of candy bars and wants to select 3 of them to display. The order in which the boxes are arranged does not matter in this case.
The formula for combinations is:
C(n, r) = n! / [r!(n-r)!]
where:
- n is the total number of options,
- r is the number of options to choose,
- "!" denotes a factorial, meaning the product of all positive integers up to that number.
Substituting the given values into the formula:
C(5, 3) = 5! / [3!(5-3)!] = (54321) / [(321)(21)] = 120 / [6*2] = 120 / 12 = 10
So, there are 10 possible arrangements of 3 different candy bar boxes.
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