MTH 245 WHW 6
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Oregon State University, Corvallis *
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Course
245
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
2
Uploaded by jingleheimerjohn21
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MTH 245 Written Homework #6 Combinatorics and Counting Methods
Learning Objectives: • Solve counting problems using various methods • Find the number of permutations of n distinct objects using the multiplication principle • Find the number of permutations of n non-distinct objects • Find the number of permutations of n distinct objects using the formula • Find the number of combinations using the formula Problem #1 Celina is picking a new frame for a custom piece of artwork. She has to select a frame size, material, and color. There are four di
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erent frame sizes, three di
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erent frame materials, and six di
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erent frame colors. She must chose one option only from each category. How many di
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erent possible frames could Celina pick from?
Problem #2 There are 15 candidates running for any of 5 distinct positions on the local school board. In how many di
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erent ways could the 5 positions be filled?
Problem #3 I have 15 outfits to select from to pack for my business trip. I would like to select three of them to pack in my suitcase. How many packing possibilities are there?
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Problem #4 A local company has a 6 person management team and 20 employees. The company needs to select 3 people from the management team and 7 employees to attend a regional meeting. How many di
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erent possibilities are there for the group that can be sent to the regional meeting?
Problem #5 Suppose you flip a two sided fair coin (“heads” or “tails”) 8 total times. a). How many ways result in 6 tails and 2 heads?
b). How many ways result in 2 tails and 6 heads?
c). Compare your answers to part (a) and (b) and explain in a few sentences why the comparison makes sense.
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