Respuesta :
Using the permutations formula, it is found that: 11,232,000 different license plates are possible
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The order in which the letters and the numbers appear is important(123ABC is a different plate than A123BC), which means that the permutations formula is used to solve this question.
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Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
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In this question:
- 3 letters from a set of 26.
- 3 digits from a set of 10.
Thus:
[tex]T = P_{26,3}P_{10,3} = \frac{26!}{23!}\times\frac{10!}{7!} = 11,232,000[/tex]
11,232,000 different license plates are possible
A similar problem is given at https://brainly.com/question/16812463
