A camp offers 4 different activities for an elective: archery, hiking, crafts and swimming. The capacity in each activity is limited so that at most 35 kids can do archery, 20 can do hiking, 25 can do crafts and 20 can do swimming. There are 100 kids in the camp. How many ways are there to assign the kids to the activities

There are 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:

Where 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, is 35, is 20, is 20 and is 25.

Finally, replacing values, we get:

So, There are ways to assign the kids to the 4 activities.

square pyramid

step-by-step explanation:

square prism looks like nothing like that

triangular prism has a rectangular base instead of a square base

tetrahedron has a triangular base