Answer to Question #336363 in Discrete Mathematics for ysa

Question

1. A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 6 science courses, any of 4 humanities, and any of 4 mathematics courses, how many ways can she arrange her program?

2. The store at your school wants to stock sweatshirts that come in four sizes (small, medium, large, extra-large) and in two colors (red and white). How many different types of sweatshirts will the store have to stock?

3. Rysel received a new wardrobe consisting of 6 shirts, 4 pairs of pants, 2 skirts, and 3 pairs of shoes for her birthday. How many new outfits can she make?

Answer 1

$C^1_6C^1_4C^1_4=6x4x4=96$

2. $C^1_4C^1_2=4x2=8$

3. Shirt she can use with pants or skirts. So $C^1_6C^1_4C^1_3+C^1_6C^1_2C^1_3=6x4x3+6x2x3=72+36=108$