How many different license plates are possible if two digits are followed by three letters?

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How many license plates are possible if four letters are to be followed by two digits?

it 26 to the power 4 and then 99 for the numbers figure that out add the two together

A license plate consists of 1 letter excluding O and you followed by a 4-digit number that cannot have a 0 in the lead position How many different plates are possible?

There can be 26*9*10*10*10 = 234000 different plates. This assumes that the letter can be I (which may be confused with 1) or Z (2).

How many different license plates exist if each license plate contains 3 letters and 4 numbers and all four numbers are even?

384,475,000 license plates. There are 35 different letter/number combinations possible. Each combination has 10,985,000 variants. 35*10,985,000 = 384,475,000

How would you solve a problem like this License plates in Oregon consist of three letters followed by three digits How many possible Oregon license plates are there?

Multiply the possibilities for each digit: 26 * 26 * 26 * 10 * 10 * 10 = 17,576,000

How many license plates can be made using either three digits followed by three letters or three letters followed by three digits?

35,152,000 (assuming that 000 is a valid number, and that no letter combinations are disallowed for offensive connotations.) Also, no letters are disallowed because of possible confusion between letters and numbers eg 0 and O.

The number of arrangements of three letters followed by three digits is $26^3\cdot 10^3$, seen by direct application of the rule of product using the following steps:

• Pick what the letter is in the first spot (26 choices)
• Pick what the letter is in the second spot (26 choices)
• Pick what the letter is in the third spot (26 choices)
• Pick what the digit is in the fourth spot (10 choices)
• Pick what the digit is in the fifth spot (10 choices)
• Pick what the digit is in the sixth spot (10 choices)

The total number of arrangements of three letters followed by three digits is then the product of the number of options available at each step and is then $26\cdot 26\cdot 26\cdot 10\cdot 10\cdot 10=26^3\cdot 10^3$.

IF we were to assume that every license plate consists of three letters followed by three digits in that specific order and that each such arrangement is equally likely to occur, then the probability that we correctly guess what is on the license plate assuming we guess a valid string of three letters followed by three digits will be $\frac{1}{26^3\cdot 10^3}$.

If we were to guess that the license plate contains the entire work of Shakespeare and a picture of a cow jumping over the moon though, then the probability that our guess was correct will of course be zero. Similarly so if we were to guess that the license plate was any invalid string of characters, which would in this case include things like $A1B2C3$ since this is not a string of three letters followed by three digits.

If we were to instead make the assumption that every license plate consists of three letters and three digits but these characters may appear in any order and each such arrangement is equally likely to occur, then we no longer have just $26^3\cdot 10^3$ possibilities. Rather, we approach as before with rule of product but this time also include the step "Choose which spaces in the license plate are the ones occupied by letters" and slightly reword things to work for our new situation (e.g. pick which letter occupies the furthest left available space designated for letters, etc...). The total number of arrangements in this scenario would instead be $\binom{6}{3}\cdot 26^3\cdot 10^3$.

Here still, the probability that a license plate has the entire collection of poems by Robert Frost is going to be zero as that is not a valid string of characters., but the probability that a randomly generated license plate matches a valid guess will be $\frac{1}{\binom{6}{3}\cdot 26^3\cdot 10^3}$ and that includes guesses like $AAA123$.

This problem is listed as 'Elementary Math', so I will keep the answer very straight forward.

The license plate has 6 spaces available: 3 for letters and 3 for digits. There are 26 letters available in the alphabet (A-Z) and 10 digits available (0-9). They key to this problem is that repetition is not allowed for either the letters or the numbers.

(1) There are 26 possible letters that can be used in the first space. After one letter is used in the first space, since repetition is not allowed, there are 25 possible letters that can be used in the second space. Following the same logic, there are 24 possible letters that can be used in the third space.

The total number of possible combinations for the first three spaces in the license plate is 26 * 25 * 24 = 15,600.

The same logic as (1) can be applied to the last three digits in the license plate, and the final two numbers can be multiplied together to find the answer to the problem.

Hopefully this clarifies how to approach the problem and you can solve the rest on your own!

Solution:

Given, license plates consist of 3 letters followed by 2 digits.

Let the numbers on license plates be N

Let the letters on license plates be L

So, the license plate consisting of 3 letters and 2 digits will be LLLNN.

Letters can be anything from A to Z.

There are 26 letter combinations for the first letter. Again second and third letters can be anything from the 26 letters.

So, combination for letters = 26 × 26 × 26

= 17576

Numbers can be anything from 0 to 9.

There are 10 combinations for each place.

So, the combination for numbers = 10 × 10 = 100

Now, the combination for letters and numbers = 17576 × 100 = 1757600.

Therefore, 1757600 license plates can be made.

How many license plates can be made consisting of 3 letters followed by 2 digits?

Summary:

1757600 license plates can be made consisting of 3 letters followed by 2 digits.

We have #1,757,600# combinations available for license plates.

Number on license plates are of the form #LLLDD#, where #L# represents a letter and #D# represents a digit.

As #L# can be anything from #A# to #Z#, there are #26# combinations for that and as repetition is allowed,

for second and third letters, we again have #26# combinations available and thus #26xx26xx26=17576# combinations for letters.

But digits are from #0# to #9# i.e. #10# combinations for each place and tolal #10xx10=100# combinations.

Hence for #LLLDD#, we have #1,757,600# combinations available for license plates.

How many different license plates are possible if two digits are followed by three letters?

1757600 license plates can be made consisting of 3 letters followed by 2 digits.

How many license plate combinations are possible if you can use 3 letters and 2 digits letters and numbers Cannot be repeated?

As L can be anything from A to Z , there are 26 combinations for that and as repetition is allowed, for second and third letters, we again have 26 combinations available and thus 26×26×26=17576 combinations for letters. But digits are from 0 to 9 i.e. 10 combinations for each place and tolal 10×10=100 combinations.

How many different Licence plates can be made using two letters followed by three digits if neither the letters nor the digits can be repeated?

1 Expert Answer The combination of letters and numbers would just be 626 x 1000 or 626,000 different license plates.

How many different Licence plates can be made using two letters followed by two digits if both the letters and the digits can be repeated?

Combining these results, it follows that there are 676 x 1000 = 676,000 different license plates possible.

How many license plates can be made consisting of three letters followed by two digits?

How many license plates with 3 letters followed by 3 digits exist if exactly one of the digits is 1 Repeating letters and digits is allowed?

How many license plates can be made using either 3 digits followed by 3 letters or 3 letters followed by 3 digits?

How many combinations are there with 3 letters and 3 numbers?