How many license plates can be made consisting of 2 letters followed by 4 digits?
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The key observation that we need to deal with the ordering constraints is that there are $\binom{n}{k}$ ways to choose $k$ distinct elements out of $n$, and that for each of those choices there is only one way to arrange the $k$ elements so that they are ordered. Hence $\binom{26}{2}$ counts the ways to pick two letters in alphabetic order, and $\binom{10}{4}$ counts the ways to pick four digits in descending order. Show
If the first digit is allowed to be $0$, $\binom{10}{4}$ is also the number of ways to pick four digits in ascending order. This assumption is likely to hold for license plates; otherwise, $10$ must be replaced by $9$. The solution that you already know tells you how to deal with distinct, but not ordered elements. If letters and digits may come in any order, for every choice of two distinct letters and four distinct digits there are $6!$ ways to arrange them. When the letters come before the digits, we reason similarly, but we separately count the ways to fill the letter positions and the ways to fill the digit positions. For example, if the letters only need to be distinct, while the digits must be in decreasing order, we get $\binom{26}{2} \cdot 2! \cdot \binom{10}{4}$. Do you see how to continue? Statistics Question Be ny V. I need help Follow • 3 Add comment More
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Arthur D. answered • 10/29/15 Tutor 5.0 (143) Forty Year Educator: Classroom, Summer School, Substitute, Tutor About this tutor › About this tutor › letter letter digit digit 26 * 26 * 10 * 10=67,600 license plates Upvote • 1 Downvote Add comment More Report
Mayuran K. answered • 10/29/15 Tutor 4.8 (24) Patient and effective UH grad for High school Math tutoring See tutors like this See tutors like this The answer would be = 2^2 = 4 since repetition is allowed the number of licence plates you could make is 4. Upvote • 0 Downvote Add comment More Report Still looking for help? Get the right answer, fast.Ask a question for free Get a free answer to a quick problem. ORFind an Online Tutor Now Choose an expert and meet online. No packages or subscriptions, pay only for the time you need. 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.
How many license plates of 4 symbols can be made using 2 letters and 2 digits?How many license plates of 4 symbols can be made using 2 letters and 2 digits? The answer is 405,600.
How many license plates can be made using 2 letters followed by 3 digits?So for a license plate which has 2 letters and 3 digits, there are: 26×26×10×10×10=676,000 possibilities.
How many license plates can be made with 2 letters and 2 digits?2 Answers By Expert Tutors
since repetition is allowed the number of licence plates you could make is 4.
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