Answer :
Final answer:
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