Probability - A Beginner's Guide To Permutations And Combinations: The Classic Equations, Better Explained by Hartshorn Scott

Author:Hartshorn, Scott [Hartshorn, Scott]
Language: eng
Format: epub
Published: 2016-10-06T00:00:00+00:00

The equations and results for all of those are

So there are 135,597 total hands that could come that would give you a flush. That is out of possible 2,118,760 total hands. That means the odds of getting a flush with two suited starting cards are 135,597 / 2,118,760 = .064 or approximately 6.4 %

Example 6: Urn Problems

Urn problems are a classic permutation / combination type of problem. They involve drawing items out of an urn or bag. Those items are distinguished in different ways, often by color. A simple urn problem is:

You have an urn with 3 different colors of balls, red, green, and blue. There is an unlimited quantity of balls of each of the 3 colors. You draw out 5 balls. How many different arrangements of colors can you have? Assume that the order of the balls matters.

The answer to this problem is straight forwards, and doesn’t use the permutation or combination equations that we have used before. The key differentiator that informs us not to use those equations was the unlimited quantity of balls. Essentially this is the same as using a random number generator to come up with 1 of 3 numbers for each of the 5 trials.

Since for each of the 5 trials there are 3 possible options, the number of different outcomes is

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