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.

720

step-by-step explanation:

first i did work 2nd i did work and 3rd i did work

i hope this is what you were looking for.

see attached graph