In how many ways can Kala choose the classes to take?

Question

Kala, a college freshman, is deciding on classes for her first term. She can choose to take some or none of the six classes from the list below. She can't take all of them.

Astronomy, Biology, Chemistry, Dance, Economics, Geography

In how many different ways can Kala choose the classes to take? (The order of the classes chosen doesn't matter.)

Answer 1

Kala can take from 0 to 5 classes out of courses labeled A, B, C, D , E, G; 6 classes.

She can choose 0 of the classes 1 way.

She can choose 1 of the classes 6 ways.

She can choose 2 of the classes 15 ways (6 ways to choose the first and 5 ways to choose the 2nd divided by two for double counting, A,B and B, A are the same).

She can choose 3 of the classes 20 ways (6 ways to choose the first and 5 ways to choose the 2nd, 4 ways to choose the 4th; the pattern is 6!/[(6-number chosen)!*number chosen!] in this case 6!/[(6-3)!*3!].

She can choose 4 classes 15 ways

She can choose 5 classes 6 ways.

That means she can create 1 + 6 + 15+ 20 +15 + 6 = 63 different class selections of from 0 to 5 classes out of 6.