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“The factorial of n is denoted by n! and calculated by the product of integer numbers from 1 to n” For n>0, n! = 1×2×3×4×...×n For n=0, 0! = 1 Huh?

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1! = 1 2! = 2x1= 2 3! = 3x2x1 = 6 4! = 4x3x2x1 = 24 5! = 5x4x3x2x1 = 120 You simply multiply the numbers of whichever “n” you have.

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Sherlock Holmes is investigating a crime at a local office building after hours. In order to enter a building, he must guess the door code. If only one number opens the door, how many different ways can Sherlock open the door?

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1234512345 5 ways!

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If two numbers will open the door, list the different combinations of buttons that would open the door. (Assume no repetitions, i.e 3,3 ) Example: (1, 2), (1, 3), (1, 4)… 1,2 1,31,41,52,12,32,42,5 3,13,23,43,54,14,24,34,5 5,15,25,35,4

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How many ways could Sherlock open the door if two buttons will unlock it? 20 ways! How many possible choices? 5 Now, how many possible choices? 4

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If three numbers will open the door, list the different combinations of buttons that would open the door. (Assume no repetitions) Example: (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 5)… 1,2,31,2,41,2,51,3,2… There has to be another way…

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How many different ways could Sherlock open the door if three buttons will unlock it? A grand total of 60 ways to unlock that door

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This does mean that if you now need to use FOUR buttons, it will be: Again, the 5 does not mean you selected “button #5,” it means that you have 5 buttons to choose from. Since no repetition, then you would now have 4 buttons to choose from and 3 and so on.

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Permutation: Number of arrangements when order MATTERS n = number of items r = number of choices a, b, c is DIFFERENT than a, c, b

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…in a nice way, of course Please swap notes to check if your neighbor wrote down the following correct! n = number of items r = number of choices

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n Factorial Number of Permutations N Factorial For any positive integer n, n! = n(n-1)(n-2)… 3.2.1

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#7 The ski club with ten members is to choose three officers captain, co-captain & secretary, how many ways can those offices be filled? We can of multiplication and division

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#11 In the Long Beach Air Race six planes are entered and there are no ties, in how many ways can the first three finishers come in?

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From this same worksheet, ## 1 – 3 and 7 – 13 only DO NOT forget that you need to have finished your graphs printed from online by Wednesday. This means that your calculations for your all equations need to be 100% correct. I will be available after school tomorrow for assistance.

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