DrBrain824

This equals (2^3)^2 - (3^2)^3 = 2^6 - 3^6 = 64 - 729 = -665. 

First lets choose the stars on the court. 

3 choose 2 = 3 * 2/2 * 1 = 3

Now, out of the 8 players left, 3 of them need to be on the court. 

8 choose 3 = 8 * 7 * 6/6 = 56

56 * 3 = 168

There are 168 possibilities. 

The number of total arrangements is 8!/4 * 2! = 8! / 8 = 7! = 5040. 

There are 5040 total arrangements.

The number of arrangements in which the first four balloons have different colors is 4! * 4! = 24 * 24 = 576. 

There are 576 total arrangements.

Hope this helped!!

We can use PIE, (Principle of Inclusion - Exclusion)

We can add 48 + 39 + 35 = 122, but this is over counting since some people took 2 or even 3 classes. 

From 122, we need to subtract 20 + 19 + 22 = 61.

But we need to add 10 back to count the ones who took all the classes. 

61 + 10 = 71. 

100 - 71 = 29

29 students did not enroll in any of the subjects. 

Out of the 18 people, 2 of them will be on the decoration committee. 

18 choose 2 = 18 * 17 / 2 = 9 * 17 = 153

Then out of the 2 people chosen, on will be the leader. 

2 choose 1 = 2/1 = 2

153 * 2 = 306

There are 306 ways the committee can be choosen. 

The only cube that has no red paint is the one in the middle of the cube. 

Since there are 27 cubes, (3 * 3 * 3), 27 - 1 = 26 cubes that have red paint. 

The question is just asking how many ways to order the kids. 

3! = 6

There are 6 ways.