Answer:
Hi,
Explanation:
To find the number of different standard license plates possible in this system, we can break down the problem step by step.
How many different standard plates are possible in this system?
First, let's consider each part of the license plate:
3 numbers: Since repetitions are not allowed, we have
10 choices for the first number (0-9),
9 choices for the second number (excluding the first one), and
8 choices for the third number.
This results in 10×9×810×9×8 possibilities for the numbers
3 letters: With 26 letters in the alphabet and no repetitions allowed, we have
26 choices for the first letter,
25 choices for the second letter (excluding the first one), and
24 choices for the third letter. This gives us 26×25×2426×25×24 possibilities for the letters.
2 numbers: Again, for the numbers, we have
10 choices for the first number and
9 choices for the second number.
Now, we can find the total number of different plates by multiplying the possibilities for each part:
10×9×8×26×25×24×10×9=1010880000
How many different standard plates are possible in this system if the last number must be an even number?
For this scenario, we will keep everything the same as in the previous calculation except for the last part, where the last number must be even.
2 numbers: For the last number, we have 5 choices (0, 2, 4, 6, 8) because we want it to be even. The other number has 10 choices (0-9)
but we may not have 00,22,44,55,88 : substract 5
Now, we can calculate the total number of different plates with an even last number:
10×9×8×26×25×24×(5×10-5)=505440000