Question

Question content area top part 1 a group of campers is going to occupy 6 campsites at a campground. there are 15 campsites from which to choose. in how many ways can the campsites be​ chosen?

Answer 1

To determine the number of ways to choose 6 campsites from 15, the combination formula C(n, k) = n! / (k!(n-k)!) is used, which in this case is C(15, 6) = 15! / (6!9!).

Step-by-step explanation:

The question asks in how many ways 6 campsites can be chosen from a total of 15 available campsites. This scenario can be solved using combinations, a concept from combinatorics, which is a branch of mathematics that deals with counting combinations and permutations. Since the order in which the campsites are chosen does not matter, we use the combination formula: C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from and k is the number of items to choose.

To find the number of ways to choose 6 campsites from 15, we can apply the formula as follows:

1. 
   
3. Calculate the factorial of the total number of campsites (n = 15): 15!
4. 
   
6. Calculate the factorial of the number of campsites to choose (k = 6): 6!
7. 
   
9. Calculate the factorial of the difference between the total number and the chosen number (n - k = 15 - 6): 9!
10. 
    
12. Insert these values into the combination formula to get C(15, 6) = 15! / (6!9!)
13. 
    
15. Compute the result to find the total number of combinations.

The computation yields the number of ways the campers can choose their 6 campsites from the available 15.