I work through the Fundamental Counting Principle at the beginning of the lesson. At 6:03 I use the idea of playing the lottery to develop the idea of Permutations and Combinations. At 15:00 I give the formulas for Permutations nPr and Combinations nCr and work through two last examples.
I have no quibble with your method of instruction. You were quite clear and very thorough; however, there was an issue of terminology that bothered me. You kept using the phrase 'odds of winning,' when what you calculated was actually the probability of winning. Odds and probability are not the same thing.
Granted, when the probability of winning is very low, as in this case, the odds of winning and the probability of winning have approximately the same value but they are nonetheless not the same concept. Odds is a ratio that bookmakers use to handicap horse races, and it is usually stated in terms of 'odds against winning' rather than 'odds of winning.' Odds...against... are the number of times that you should expect to lose vs. the number of times you expect to win. Odds...of winning... then is the inverse of odds...against.
If an event has a probability p that you'll win, it also has a probability 1 - p that you'll lose. The odds...against winning... are
(1-p)/p. Simplifying this expression, Odds = 1/(p - 1). When 1/p is greater than 1, the trailing constant may be safely neglected, and the Odds ...against winning... become approximately 1/p. Flipping this ratio upside-down, the odds... of winning... are likewise approximately equal p. Probability and odds may be approximately equal but they are not the same thing.
Check out http://www.ProfRobBob.com, there you will find my lessons organized by class/subject and then by topics within each class. Find free review test, useful notes and more at http://www.mathplane.com
Tagged under: Combination,Permutation,counting principle,nPr,nCr,permutations combinations,rule product,Mathematics (Field Of Study)
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