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A Newfoundland & Labrador license plate consists of of three letters followed by three digits (ex ABC-123). If there are no restrictions on the letters or digit...

Question

A Newfoundland & Labrador license plate consists of of three letters followed by three digits (ex ABC-123). If there are no restrictions on the letters or digits, how many different NL license could be created?01) 29,312,0002) 8,468,0003) 2,600,0004) 17,576,0005) 2,340

A Newfoundland & Labrador license plate consists of of three letters followed by three digits (ex ABC-123). If there are no restrictions on the letters or digits, how many different NL license could be created? 01) 29,312,000 2) 8,468,000 3) 2,600,000 4) 17,576,000 5) 2,340



Answers

How many different license plates can be formed by using any 3 letters followed by any 3 digits? How many if we allow either the 3 digits or the 3 letters to come first?

We're being asked to find how many different license plates weaken get. If each contains three letters. It's a straight line. Three letters and then those three letters air followed by three digits. Okay, that's the first question will deal with the second question with repeats in such afterwards. So three letters in the first blank are in the first three blanks. All right, well, how many letters are there in the alphabet? There are 26. So that would mean there are 26 possible letters that we could have in the first three spots of the license plate. Then the last three blanks are reserved. Four digits. Well, how many digits are possible? They have to be single digits. So that's just 012345678 and nine. We can't do 10 or higher, so that would be 10 possible digits, which means to get our total. We simply just need to take 26 times, 26 times, 26 times, 10 times, 10 times 10, right. So if we take 26 times 26 times 26 or effectively 26 to the third, and then we multiply that by 10 times, 10 times 10 or effectively 10 to the third. We get one. Nope. Sorry. 17 million 576,000 possible combinations. Possible license plates, which is a lot of different license plates. But then it asks us a separate question. It says, How many of these license plates contained no repeated letters and no repeated digits? Okay, well, that's a bit of a separate question then. So again, we're doing license plates where there are three letters and three numbers. So if we think about those letters, we'd have 26 options to begin with again. But whatever letter we pick for that first blank now, we're not allowed to repeat it. So that means we only have 25 possible letters left for our second blank because one of them was used in the first one. And that would mean for our third blank on the license plate, we only have 24 possibilities because we've already used to of our 26 letters, and we're not allowed to repeat same idea for the digits. We start off with 10 possible digits, zero through nine, but then we're going to use one of those and once we have used one of those, we can't use it again. So now there's only nine possibilities. And then finally, we've used two of our digits. So there's only gonna be eight of our original 10 available for us to choose from in our last spot. But we still just have to multiply these together, so the math behind it isn't super tough. You're just kind of plug into your calculator. You're gonna take 26 times, 25 times 24 and then times 10, um, times nine times eight. And if you do that, you will get 11 million 232 1000 license plates. So that's still a fair amount, but certainly far less than 17 million. And that's how maney license plates with no repeats. Or you could say that's how many unique license plates you can make is another term that could be used sometimes

Great. So for the first part of the problem, we're figuring out the number of different license plates possible. If you have three digits, one letter and then three digits, so they're 10 digits available, the number zero through nine. So for each of the digits you have 10 choices, and then in our alphabet we have 26 letters. So for the letter, we have 26 choices. So when we multiply all of those together, we get 26 million. Now. The second part of the problem says how many license plates are possible if the letter can actually occur anywhere except last, so the letter could be first or second or third or fourth or fifth or sixth. So we have six choices for where the letter is, and then we would multiply that by the number of license plates available that we found in Part one. So we have six times 26 million, and that works out to be 156 million

We want to answer the question how many license plates can be made using? Either three digits followed by three uppercase english letters or three uppercase english letters followed by three digits. So the way that we can do this is first of all recognize that we're going to end up with essentially the same set of possibilities. Just repeated. Um you know, we we can have a particular number of just without reference to order three digits and three letters here we're saying okay, it could be three digits than three letters or three letters than three digits and we're counting those different orders as being separate entities. So we can do two times and then figure out the number regardless of order. So it will be two times. Well then we need to figure out how many different possible combinations of three digits in three letters can there be? Well there are 10 different digits, We have three. So we're going to have 10 to the power of ST And then there are 26 different English letters And we will choose three. So we'll have 26 to the power of three. So I have two times 10 to the power of three times 26 to the power of three, Which is going to be 35 million 152,000.

In this problem, we have been asked to determine how many different license plate numbers can be made if one letter is used and that is followed by five digits selected from the digits zero through nine. So we can see that there will be one letter and then five digits. So there will be a total of six places in the license plate number. Now the first one will be A light will be a letter. Now there are a total of 26 letters. So there are a total of 26 options for the first character of this license plate number And it is followed by five digits selected from the digits 0- nine. So there are 10 digits and thus there will be 10 options for each of the following five characters of the license plate number. So by using the multiplication rule of counting the total number of license plate numbers that can be formed, we obtained by multiplying these numbers So we will have 26 times 10 to the power, five Or 26, followed by five Zeros. So the total number of license plate numbers that can be made will be Equal to 2,600,000.


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