Answer:
There are [tex]9.837*10^{55}[/tex] ways to assign the kids to the activities
Step-by-step explanation:
the number of ways in which we can assign n elements into k groups is calculated as:
[tex]\frac{n!}{n_1!n_2!...n_k!}[/tex]
Where [tex]n_i[/tex] is the number of elements of every group and i goes from 1 to k.
Now, there are 100 kids in the camp and we need to assign them into 4 different activities and at most 35 kids can do archery, 20 can do hiking, 25 can do crafts and 20 can do swimming. So, it means that n is equal to 100, k is equal to 4, [tex]n_1[/tex] is 35, [tex]n_2[/tex] is 20, [tex]n_3[/tex] is 20 and [tex]n_4[/tex] is 25.
Finally, replacing values, we get:
[tex]\frac{100!}{35!*20!*25!*20!} =9.837*10^{55}[/tex]
So, There are [tex]9.837*10^{55}[/tex] ways to assign the kids to the 4 activities.
