- CFA Exams
- CFA Level I Exam
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 10. Principles of Counting

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**CFA Practice Question**

How many three-digit numbers can you form using the digits 1, 3, 5, 7, and 9 without a repeating a digit within the number to be formed?

A. 20

B. 60

C. 125

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**User Contributed Comments**
9

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

haarlemmer |
The solution choose 3 out of 5 5C3 this three number can be arranged in order 3! the answer 5C3*3! |

johnsk |
It's a permutation: 135 != 315 so the order does matter. 3P5 = 5!/(5-3)! = 60. |

Eckhardt1978 |
5!/(5-3)! |

armanaziz |
Note: nPr = n!/(n-r)! nCr = n!/(n-r)!r! |

dealsoutlook |
its 5P3 and not 3P5 |

sheenalim |
ok, what if the number to be formed can have only 2 repeated digits? i think the answer would be: 5 x 4 x 4 = 80 correct me if i'm wrong. |

clarelau |
Sheennalim: Repeated digits are not allowed. SO either 335 or 333 is incorrect. It's 5P3=60 |

peteypete |
you dont need the nPr just 5x4x3 |

Rsanches |
5!/(5-3)!=60 |