A bakery has 8 types of cupcakes. A customer purchases 2 different types of cupcakes. Determine how many 2-cupcake orders a customer can purchase. 720 56 28 16
Question
A bakery has 8 types of cupcakes. A customer purchases 2 different types of cupcakes. Determine how many 2-cupcake orders a customer can purchase.
Options:
- 720
- 56
- 28
- 16
Solution
This is a combination problem. The customer is choosing 2 cupcakes out of 8, and the order in which the cupcakes are chosen doesn't 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 chosen, and "!" denotes a factorial, which means multiplying all positive integers up to that number.
Here, n = 8 (the total types of cupcakes) and k = 2 (the number of cupcakes chosen).
So, C(8, 2) = 8! / [2!(8-2)!]
= (87654321) / [(21)(654321)]
= (87) / (21)
= 28
So, a customer can purchase 28 different 2-cupcake orders.
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