- CFA Exams
- CFA Exam: Level I 2021
- Study Session 2. Quantitative Methods (1)
- Reading 8. Probability Concepts
- Subject 10. Principles of Counting

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**CFA Practice Question**

How many license plates are possible if each consists of three letters followed by three digits? Repetition is permitted.

B. 12,812,904

C. 17,576,000

A. 108

B. 12,812,904

C. 17,576,000

Correct Answer: C

26 x 26 x 26 x 10 x 10 x 10 = 17,576,000

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**User Contributed Comments**
12

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

Will1868 |
26^3*10^3=17,576,000 |

stevelaz |
can someone please explain this? |

stevelaz |
Got It...26 letters and 10 numbers (0-9 inc) |

chamad |
I thought the permutation rule applies : 3P26(for letters) * 3P9(For numbers)?! |

chamad |
They applied the combination formula. Why not the permutation? I think the order does matter for Licence plates. Does'nt it? |

got2pass |
the question specifically states that the order be letters for the first three, and then numbers for the last three digits |

vinooka |
You have six slots to fill - - - - - - The first slot can be filled by a one of 26 letters - so 26 ways. Second slot again can be filled in 26 different ways (since repetition is allowed...otherwise it's only 25) similarly, third - 26, Fourth - 10, Fifth - 10, Sixth - 10 26x26x26x10x10x10 |

vinooka |
if repetition is not allowed, then the answer would be - 26x25x24x10x9x8 = 11232000 |

tshepi |
how did you get 26? |

Nomni |
26 alphabet letters and 10 number |

ashish100 |
what if english isn't your first language? how's a candidate expected to know how many letters in the english alphabet! |

renataa |
ive never even counted the letters in the alphabet of my mother language.... |