Question

You are ordering 100 muffins. The buisness allows you to choose 5 different kinds out of their 12 kinds. How many ways can you choose 5 types of muffins from a variety of 12 types

Answer 1

There are 792 different ways to choose 5 types of muffins from a selection of 12 types, calculated using the combinations formula.

Step-by-step explanation:

To determine the number of ways to choose 5 types of muffins from 12 available types, we use the concept of combinations in mathematics. Combinations allow us to find the number of ways to choose a subset when the order of selection does not matter. In this case, we are choosing 5 muffins from 12, without regard to the order in which we select them.

The formula for combinations is denoted as nCr, which stands for the number of combinations of n items taken r at a time. This is mathematically expressed as nCr = n! / (r!(n-r)!), where n! (n factorial) is the product of all positive integers up to n, and r! is the factorial of r.

Using this formula, we can calculate the number of ways to choose 5 types of muffins from 12 types as follows:

12C5 = 12! / (5!(12-5)!) = 12! / (5!7!) = (12×11×10×9×8) / (5×4×3×2×1) = 792

Therefore, there are 792 different ways to choose 5 types of muffins from a selection of 12 types.