please solve from \'f\' to \'k\' Problem 4 A car plate in the state of Minnesota
ID: 3304630 • Letter: P
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please solve from 'f' to 'k'
Problem 4 A car plate in the state of Minnesota consist of three digits followed by three characters. (a) Find the total number of plates can be issued by the MN DMV (b) Find the number of plates who have an A at their 4th position. (c) Find the number of plates who have at least one A (d) Find the number of plates with three consecutive three digits in increasing order, i.e., 012, 123,...,789. (e) How many plates with no repeated symbols (digitsletter) does exist? () How many plates with letters in (U, V, W. x, Y, Z) does exist? Now, assume DMV issues the plate according to a uniform distribution, i.e, issuing all possible plates are equally likely (g) What is the chance of getting a plate with at least one A? (h) What is your chance to get a plate with three letters consistent with your F.M.L. (first name, middle name last name) in the right order? (i) What is the chance of seeing a plate with first digit being (strictly) less than the second one? G) A dirty car just passed by yours, and you only saw a 4 at its second digit. What is the probability that its first (lk) If someone tells you that in her car's plate the first digit is strictly less than the second one, what is the digit being (strictly) less than the second one? chance that her second digit is 4?Explanation / Answer
We are allowed to do 4 subparts question at a time. Post again for more subparts of question.
a) No of plates = 10 * 10 * 10 * 26 * 26 * 26 = 17576000
b) A at 4th position.
Number = 10 * 10 * 10 * 1 * 26 * 26 = 676000
c) At least one A = Total - No As
Number = 17576000 - 10 * 10 * 10 * 25^3
Number = 1951000
d) Digits in increasing order:
Total ways digits can be arranged = 8
Number = 8 * 26^3 = 140608
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