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Question: 199
1. When getting ready in the morning, Marc selects his outfit from among four pairs of pants, six shirts, and two pairs of shoes. If each outfit includes one pair of pants, one shirt, and one pair of shoes, how many different outfits can Marc make?
A. 12 B. 20 C. 27 D. 48
E. 54
Correct Answer: D
Explanation:
D. You want to use the counting principle to solve this question. (See Chapter 18 for a refresher on probability.) The counting principle tells you that when multiple events appear in a problem, the total number of possibilities is the product of the number of possibilities for each event. In this problem, you have three events: choosing a pair of pants (four possibilities), choosing a shirt (six possibilities), and choosing a pair of shoes (two possibilities). Therefore, you know that 4 × 6 × 2 = 48 different outfits you can make.
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Morgan V.
asked • 05/13/19
Jon is packing for a trip. He has packed 2 pairs of pants, 4 shirts, and 2 pairs of shoes. In the space below, create a tree diagram, table, or list to show the sample space representing his outfit combinations and determine how many outfits can be made.
2 Answers By Expert Tutors
Ari H. answered • 05/13/19
Ready to tutor almost anything - San Diego, south bay, & Rosarito.
Jon could wear pants1 or pants2. No matter which pants he wears, he has four shirts to choose from, so the combinations look like this:
pants1 shirt1
pants1 shirt2
pants1 shirt3
pants1 shirt4
pants2 shirt1
pants2 shirt2
pants2 shirt3
pants2 shirt4
That's eight combinations. 2 pants * 4 shirts = 8 combinations.
Now, no matter which combination he chooses, he can wear one of two pairs of shoes. Now, the combinations look like this:
pants1 shirt1 shoes1
pants1 shirt1 shoes2
pants1 shirt2 shoes1
pants1 shirt2 shoes2
pants1 shirt3 shoes1
pants1 shirt3 shoes2
pants1 shirt4 shoes1
pants1 shirt4 shoes2
pants2 shirt1 shoes1
pants2 shirt1 shoes2
pants2 shirt2 shoes1
pants2 shirt2 shoes2
pants2 shirt3 shoes1
pants2 shirt3 shoes2
pants2 shirt4 shoes1
pants2 shirt4 shoes2
That's sixteen combinations. 2 pants * 4 shirts * 2 shoes = 16 combinations.
Pants 1 shirt 1 shoes 1
Pants 1 shirt 1 shoes 2
Pants 1 shirt 2 shoes 1
Pants 1 shirt 2 shoes 2
Pants 1 shirt 3 shoes 1
Pants 1 shirt 3 shoes 2
Pants 1 shirt 4 shoes 1
Pants 1 shirt 4 shoes 2
Pants 2 shirt 1 shoes 1
Pants 2 shirt 1 shoes 2
Pants 2 shirt 2 shoes 1
Pants 2 shirt 2 shoes 2
Pants 2 shirt 3 shoes 1
Pants 2 shirt 3 shoes 2
Pants 2 shirt 4 shoes 1
Pants 2 shirt 4 shoes 2
2*4*2 = 16 combinations
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