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------------------------------------------------ In how many ways can you select 12 paintings out of a collection of 20 to hang in your art gallery?

You can select 12 paintings from a collection of 20 using the combination formula. The result is 125970 different ways. This formula is essential for calculating combinations in scenarios like this one.

Explanation:

Calculating the Selection of Paintings

To determine the number of ways to select 12 paintings from a collection of 20 paintings, we can use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

In this case, n is 20 (the total number of paintings) and r is 12 (the number of paintings to choose). Therefore, we calculate:

First, compute the factorials:

20! (20 factorial) is the product of all positive integers up to 20.

12! (12 factorial) is the product of all positive integers up to 12.

(20 - 12)! = 8! (8 factorial) is the product of all positive integers up to 8.

Now, substituting into the formula gives us:

C(20, 12) = 20! / (12! * 8!)

This equals:

C(20, 12) = 20! / (12! * 8!) = 125970

Thus, there are 125970 ways to select 12 paintings out of a total of 20 to hang in your art gallery.

Learn more about combinations here:

https://brainly.com/question/30646507