# Human Nature, Biology, and Social Structure: A Critical Look at WhatScience Can Tell Us About Society

## An Introduction to Mathematical Probability

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Permutations of objects that are not all different
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16*63 1 | 6*36 | 166*3 | 1636* | 136*6 | 1366* |

6*631 | 6*613 | 6*136 | 6*163 | 6*316 | 6*361 |

516*3 | 6136* | 6316* | 636*1 | 66*13 | 66*31 |

316*6 | 3166* | 36*16 | 36*61 | 3616* | 366*1 |

4! = 1 x 2 x 3 x 4 = _24_ = 12

2! 1 x 2 2

The number of distinct permutations of n objects of which s are alike, t are alike, etc. is

n! _

s! t! . . .

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Example
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: How many different permutations can be made using all the letters of the word Connecticut?

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Solution:
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The word Connecticut contains eleven letters including three C’s, two N’s, and two T’s. The number of different permutations of these letters is

11! = 3! x 4 x 5 X 6 x 7 x 8 x 9 x 10 x 11

3! 2! 2! | 3! x 2 x 2 |

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Exercises
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- 1.) How many different permutations can be made using all the letters of the word dinner?
- 2.) How many distinct permutations can be made using all the letters of the word (a) challenge (b) banana (c) staff (d) tuition (e) assassination (f) committee?
- 3.) How many different seven digit numbers can be made using all the seven digits 3, 3, 3, 4, 4, 5, 5?
- 4.) In how many ways can five nickels, three dimes, four pennies and a quarter be distributed among thirteen people so that each person may receive one coin?
- 5.) How many signals can be made by raising four red flags, two green flags, and one white flag on a pole at the same time?