- 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**

If there are 30 entries in a "best of breed" dog show, in how many ways can 1st, 2nd, and 3rd place be awarded?

A. 4060.

B. 30.

C. 24,360.

Correct Answer: C

_{30}P_{3}= 30!/(30 - 3)! = 24,360###
**User Contributed Comments**
8

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

nsmwaura |
But I thought order matters in this case. Dog A, B & C for 1st 2nd and 3rd respectively is not the same as dog b, a and c |

charlie |
that's why the answer uses P not C to calculate! |

krisscfa |
Its actually Different.... Step 1:- 30 C 3= 4060. Step 2:- Dogs can be arranged in 6 ways in 1st ,2nd and 3rd places So the answer is 4060*6=24,360 |

Rivermax |
1st - any of the 30 2nd - any of the remaining 29 3rd - any of the remaining 28 => 30 X 29 X 28 = 24360 |

prachirp |
I think very logical and easy to understand. Thanks Rivermax. |

hoyleng |
when to use nPr n when to use nCr? pls help. thanks |

gulfa99 |
npr when order matter and ncr vice versa |

chipster |
I like Rivermax explanation but on BAII 30-->2nd-->nPr-->3--> = gives answer |