- 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 if you are allowed to repeat any of the aforementioned digits any number of times within the number to be formed?

A. 20

B. 60

C. 125

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**User Contributed Comments**
9

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

Menzies |
5x5x5=125 Because u can reuse the numbers |

CocaColas |
Is there any more theoretical way to get to the answer other than by doing it manually? |

mtcfa |
Any five digits can be used in slot 1, any five digits can be used in slot 2, and any five digits can be used in slot 3... hope that helps. |

labsbamb |
ok good |

rahul1983 |
The number in the first place can be picked up in 5 ways. Similiarly for secon and the third place. Now to form a three digit number, you'll have to pick (number1 AND number2 AND number3). The pick of numbers is mutually exclusive to each other since repetitions are allowed. Hence the answers 5*5*5 = 125 P.S: I got the answer incorrect coz I failed to recollect my permutation and combination fundamentals |

cslau83 |
why can't we do a straight permutation calculation to get 60? |

Shaan23 |
When you do permutation the numbers are not reused again. Only can use the numbers once then |

sandk024 |
On the BAII you can use 5! by entering 5[2nd][x!] = 120 + 5 because the numbers are allowed to be repeated. |

kmurdoch |
Why is it +5 sandko24? |