A car dealership is promoting a particular model of car that has 8 optional features available. Each optional feature can be purchased separately. How many different packages of 3 optional features are possible for this model of the car?
Question
A car dealership is promoting a particular model of car that has 8 optional features available. Each optional feature can be purchased separately. How many different packages of 3 optional features are possible for this model of the car?
Solution
This is a problem of combinations in mathematics. We are choosing 3 features out of 8, and the order in which we choose them does not matter.
The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of options,
- k is the number of options to choose,
- "!" denotes factorial, which is the product of all positive integers up to that number.
Substituting the given values into the formula:
C(8, 3) = 8! / [3!(8-3)!]
= (87654321) / [(321)(54321)]
= (876) / (321)
= 56
So, there are 56 different packages of 3 optional features possible for this model of the car.
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