How many license plates of 3 symbols can be made using at least 2 letters for each
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Transcribed image text: 19. How many license plates of 3 symbols (letters and digits) can be made using at least 2 letters for each? 20. Suppose you have totally forgotten the combination to your locker. There are three numbers in the combination, and you're sure each number is different. The numbers on the lock's dial range from 0 to 35. If you test one combination every 12 seconds, how long (in days to the nearest hundredth) will it take to test all possible combinations? 21. DNA molecules include the base units adenine, thymine, cytosine, and guanine (A, T, C, and G). The sequence of base units along a strand of DNA encodes genetic information. In how many different sequences can A, T, C, and G be arranged along a short strand of DNA that has only 8 base units? 22. How many 3-letter code words can be formed if at least one of the letters is to be chosen from the vowels a, e, i, o, and u? Show
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.
#26xx26xx10xx10xx10= 676,000# possibilities There is nothing stating that the letters and numbers can't be repeated, so all #26# letters of the alphabet and all #10# digits can be used again. If the first is A, we have #26# possibilities: If the first is B, we have #26# possibilities: And so on for every letter of the alphabet. There are #26# choices for the first letter
and #26# choices for the second letter. The number of different combinations of #2# letters is: The same applies for the three digits. #10xx10xx10 =1000# So for a license plate which has #2# letters and #3# digits, there are: #26xx26xx10xx10xx10= 676,000# possibilities. Hope this helps. Answer: 37,856 Step-by-step explanation: First case: all 3 symbols are letters: 26^3 = 17,576 possible Second case: 2 letters & one digit: 10(26^2) = 6,760 by considering the one digit to be qt extreme right. But there are two other possibilities--one digit in middle & one digit at extreme left. There this accounts for 3(6760) = 20,280 possible "second case" arrangements. final answer: 17,576 + 20,280 = 37,856 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 can be made with 3 letters and 2 numbers?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 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.
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 either two letters?Combining these results, it follows that there are 676 x 1000 = 676,000 different license plates possible.
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