- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 3. Probability Concepts
- Subject 10. Principles of Counting

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**CFA Practice Question**

When you buy a one-dollar ticket for the Florida Lotto, you are trying to match six numbers drawn from 53 numbers, in any order. How many different tickets are possible?

B. 22,957,480

C.

A. 53

^{6}B. 22,957,480

C.

_{53}P_{6}Correct Answer: B

_{53}C_{6}= 53!/[(53 - 6)! x 6!] = 22,957,480###
**User Contributed Comments**
12

User |
Comment |
---|---|

ione |
isn't lotto numbers can be repeated? |

noonah |
No ione, lotto numbers cannot be repeated. |

mtcfa |
I have a BA II Plus. When I do factorials with large numbers (anything greater than 13), I get things like 2.3564849 13, which I think is scientific notation. How do I handle problems with such large numbers? |

tenny45 |
mtcfa, maybe try the format button and change the decimal places |

steved333 |
It does that because there are not enough spaces on the screen of the calculator to show the whole number.it means 2.3564849 x 10^13. That means the number is 14 digits long. |

clafleur |
just use the nPr and nCr buttons, [2nd]+ or - |

jainrajeshv |
In any order is a key word herer |

rfvo |
Ok, here it is nCr...so order does not matter...hence BAii 53 2nd nCr 6 = XXXXX |

tschorsch |
the formula results in 53! / (47! x 6!) but 53! / 47! is just 53 x 52 x 51 x 50 x 49 x 48 |

dcfa |
when order matters nPr when order does not matter, nCr |

Matt26 |
thanks dcfa |

Yrazzaq88 |
BA Plus: 53 (2nd) nCr 6 = 22,957, 480 |