MAT 131 College Mathematics
Module 5 Discussion
Please choose one of the following problems from your textbook or one of the class discussion questions and respond fully. Please use full sentences and use a minimum of 50 words in your responses to each question.
Section 11.1 25, 26, 28, 30
Section 11.2 64, 66, 68, 70, 72
Section 11.3 72, 74, 76, 78, 80
Section 11.4 74, 76, 80, 82, 84
Section 11.5 24, 26, 28, 30
This video utilizes a soccer team and a band to help understand how combinations and permutations work. Coaches sometimes assign very specific roles, such as left midfield, right midfield, and center midfield, while others just say you three go play midfield. The presenter is able to explain how this mathematically creates a large difference. Allowing the players to choose their specific positions on an 11 player team changes the possibilities from 11 x 10 x 9 x 8 to (11 x 10 x 9 x 8)/(4 x 3 x 2 x 1). The presenter then explains that Pascalâ€s Triangle can also be used to calculate combinations. For example, to find out what choosing 2 from 4 is, count down 4 rows then over 2 numbers. The same simple processes of adding numbers together produce all sorts of things that we can see around us in the world.
Class discussion questions
1. The presenter gives the formula for combinations as nCr = (n!)/((n-r)!r!). Using this formula, what is 5 choose 2?
2. Explain what the difference is between a combination and a permutation is. Explain this in your own words, without a definition or formula.
3. Itâ€s often said that one of the most difficult hands to get in poker is a royal flush consisting of a 10, Jack, Queen, King, and Ace of the same suit. Using the information about combinations, what is the probability that you will get dealt a royal flush?