Answer:
It can be created 1575 license plated with at least one three-piece palindrome.
Step-by-step explanation:
If a license plates has at least one three-piece palindrome, we have the following cases:
1. The license plate just has a palindrome in the three numbers: The number license plates for this case can be calculated using the rule of multiplication as:
<u> 5 </u>*<u> 5 </u>* <u> 1 </u>* <u> 3 </u>*<u> 3 </u>*<u> 2 </u>= 450
1st Number 2nd 3rd 1st Letter 2nd 3rd
For have a palindrome in the numbers, the first and the 3rd number need to be the same. So, we have 5 digits for the first and the 2nd Number and one digit for the 3rd Number.
On the other hand, if the palindrome is just in the numbers, the 3rd letter need to be different from the 1st. So we have 3 options for the 1st and the 2nd letter and 2 options for the 3rd letter.
At the same way, we can calculated the number of license plates for the other cases:
2. The license plate just has a palindrome in the three letters:
<u> 5 </u>*<u> 5 </u>* <u> 4 </u>* <u> 3 </u>*<u> 3 </u>*<u> 1 </u>= 900
1st Number 2nd 3rd 1st Letter 2nd 3rd
3. The license plate has a palindrome in the three numbers and in the letters:
<u> 5 </u>*<u> 5 </u>* <u> 1 </u>* <u> 3 </u>*<u> 3 </u>*<u> 1 </u>= 225
1st Number 2nd 3rd 1st Letter 2nd 3rd
Then, It can be created 1575 license plates with at least one three-piece palindrome and it is calculated as:
450 + 900 + 225 = 1575
