Answer to the Problem of the Week for the week of May 22, 2006 |
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Virginia LOTTO South |
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In the Virginia LOTTO South game, participants select six numbers from 1 to 49. You win a prize if you can match 3, 4, 5, or 6 numbers. What is the probability that a person would match none of the numbers?Answers must be expressed as a decimal (correct to four decimal places like .xxxx), a percent (correct to 2 decimal places like xx.xx%), or in the form "1 in xx.xx" (correct to 2 decimal places).
Side note: |

Solution to the Problem: |

The answer is .4360 or 43.60% or 1 in 2.29 that a person would match no numbers! First, determine the number of different combinations of 49 numbers taken 6 at a time. There are 13,983,816 different possible combinations. So, the chances of matching all six numbers are 1 in 13,983,816.Next, you must figure the number of ways in which none of the numbers matched. There are 43 numbers which do not match, so take the number of combinations of 43 numbers taken 6 at a time. This answer is 6,096,454. Now, divide these two numbers to get your answer. The probability of not matching any of the six numbers is 6,096,454 divided by 13,983,816. |

1. Leon Litvachuk |
Manual Arts High School Los Angeles, California |

2. Sagar Patel | Brookstone School Columbus, Georgia |

3. Jim Arrison | Norristown, Pennsylvania |

4. Richard Johnson | La Jolla, California |

5. Larry Schwartz | Norwalk, Connecticut |

6. Ibraheem Rasoul | Harrionburg High school Harrionburg, Virginia |

7. Ben Bassett | Washington Township High School Sewell, New Jersey |

8. Ben Reedy | ---------- |

9. Nathan Hissong | Mountain View High School Mountain View, Wyoming |

10. Paul Verschueren | Seattle, Washington |

11. Lucas Woodbury | Mountain View High School Mountain View, Wyoming |

12. Lauren Coles | Chelmsford High School Chelmsford, Massachussetts |