If a plate of car consists of a two letter and four digits and one car is chosen at random, then find the probability that the car has the letter together
actually, that's not quite right, since I did not allow for the fact that if a character is repeated, the plate count has to be reduced. See whet you can do with that.
Why did the car get an A+ in school?
Because it always had its letters together!
In this case, we need to find the probability that the car has the two letters together. There are a total of 26 letters in the alphabet, so the first letter can be any one of them. Once the first letter is chosen, there is only one more letter left that can come after it. So, the probability of the two letters being together is 1/26.
However, we also need to consider the four digits that come after the two letters. There are 10 digits from 0 to 9, so the probability of randomly selecting any one digit is 1/10. Since we need four digits together, the probability of choosing them in the correct order is (1/10)^4 = 1/10,000.
Therefore, the overall probability of randomly choosing a car with the two letters together is (1/26) * (1/10,000) = 1/260,000.
So, the probability that the car has the letters together is very slim!
To find the probability that the car has the letters together, we need to determine the total number of possible plates and the number of plates that have the two letters together.
Let's break down the problem step by step:
Step 1: Determine the total number of possible plates.
In this case, we have two letters and four digits in each plate. There are 26 letters in the alphabet and 10 digits (0-9), so the total number of possible plates is 26^2 * 10^4.
Step 2: Determine the number of plates with the two letters together.
Since there are 26 letters and we want the two letters to be together, we can treat the combination of the two letters as a single entity. So we have 25 options (excluding the two letters) for the first position and 10 options for the second position. After that, we have 24 options for the third position and 10 options for the fourth position. Therefore, the total number of plates with the two letters together is 25 * 10 * 24 * 10.
Step 3: Calculate the probability.
The probability is calculated by dividing the number of plates with the two letters together by the total number of possible plates:
Probability = (Number of plates with two letters together) / (Total number of possible plates)
Probability = (25 * 10 * 24 * 10) / (26^2 * 10^4)
Now you can simplify and calculate the probability.
To find the probability that the car has the two letters together, we need to determine the total number of possible license plates and the number of license plates that have the two letters together.
Let's break down the problem:
1. Total number of license plates:
Since the plate consists of two letters and four digits, we have a total of 26 letters in the English alphabet (excluding I and O) and 10 digits (0-9). The first letter can be any letter from A to Z (excluding I and O), and the second letter can also be any letter from A to Z (excluding I and O). Therefore, the total number of choices for the two letters is 24 * 24 = 576. The four digits can be any of the ten digits, so the total number of choices for the digits is 10,000. Therefore, the total number of possible license plates is 576 * 10,000 = 5,760,000.
2. Number of license plates with the two letters together:
To calculate the number of license plates with the two letters together, we can treat the two letters as a single entity. So effectively, we have 25 options (A to Z excluding I and O) for the combined letters, and the digits remain the same, giving us 10,000 choices. Therefore, the number of license plates with the two letters together is 25 * 10,000 = 250,000.
Now that we have the total number of choices and the number of choices with the two letters together, we can calculate the probability:
Probability = (Number of choices with the two letters together) / (Total number of choices)
Probability = 250,000 / 5,760,000
Simplifying the fraction, we get:
Probability = 25/576
So, the probability that the car has the two letters together on the license plate is 25/576.
consider the two letters as one item. Then there are
26^2 * 10^4 possible plates.
The letters and digits can be rearranged in 5! ways, so there are
26^2 * 10^4 * 5! different plates with the letters together.
There are 36^6 possible plates in all, so our probability is
(26^2 * 10^4 * 5!)/36^6 = 0.37266