A state offers specialty license plates that contain 5 numbers followed by 2 letters. License plates are assigned randomly. All

Question

2 years ago

12

license plates are equally likely. Find the number of possible license plates that can be issued using this system.

1 answer:

FrozenT [24] · Answer 1 · 2023-02-07T23:49:30+03:00

The number of possible license plates that can be issued using this system is 67600000.

<h3>What is Combination?</h3>

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements.

Here, number plate contains 5 numbers and 2 letters

Total possible number (0-9) = 10

Total possible letters (A-Z) = 26

Possible number plates which contains 5 numbers and 2 letters are

¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ¹⁰C₁ X ²⁶C₁ X ²⁶C₁

10 X 10 X 10 X 10 X 10 X 26 X 26

10⁵ X 26²

676 X 10⁵

67600000

Thus, the number of possible license plates that can be issued using this system is 67600000.

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