Answer to Question #336707 in Statistics and Probability for JB Styles

Question

Answer in (Permutation and Combination)

1. A college freshman must take a science course, a humanities course, and a mathematics course. If she may select any of 4 science courses, any of 3 humanities courses, and any of 2 mathematics courses, how many ways can she arrange her program?
2. A clothing store wants to stock sweatshirts that come in four sizes (small, medium, large, x-large) and in three colors (yellow, blue, and white). How many different types of sweatshirts will the store have to stock?
3. For her birthday, Karla received a new wardrobe consisting of 5 shirts, 3 pairs of pants, 2 skirts, and 3 pairs of shoes for her birthday. How many new outfits can she make?

Answer 1

1.

$$\dbinom{4}{1}\dbinom{3}{1}\dbinom{2}{1}=4(3)(2)=24$$

2.

$$\dbinom{4}{1}\dbinom{3}{1}=4(3)=12$$

3.

$$\dbinom{5}{1}\dbinom{3}{1}\dbinom{3}{1}+\dbinom{5}{1}\dbinom{2}{1}\dbinom{3}{1}$$

$$=5(3)(3)+5(2)(3)=75$$