Geometry-Sequences with unlimited repeated values

  • Thread starter thomasrules
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In summary, the conversation discusses how many license plates can be formed in which at least one symbol is repeated. The total possible combinations are 26^3x10^3, but the negation of this would be 26^3-25^3x10^3-9^3. However, it is stated that "unlimited repeated values" is allowed, so the original expression of 26^3x10^3 would be correct. A practical caveat is also mentioned about NY license plates having four digits instead of three, and certain letters being omitted.
  • #1
thomasrules
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Here is the question I cannot get it...

In a series of license plates, the first three symbols are any of the 26 letters in the alphabet and the last three are any of the 10 digits from 0 to 9.

How many plates can be formed in which at least one symbol is repeated?
-

--------I know that 26^3x10^3 is the total possible combinations.
I thought that you would do this: (26^3-25^3)x(10^3-9^3)
 
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  • #2
You want to know how many plates can be formed with at least one repeated symbol. Have you considered the negation? I.e. how many plates can be formed with at most zero repeated symbols?
 
  • #3
I think the expression "unlimited repeated values" simply means that you can use any letter or digit more than once so your first expression would be correct.
 
  • #4
Practical caveat. NY current plate has four digits (not three), but the first digit cannot be 0. In addition the letters I and O appear to have been omitted deliberately, looking too much like 1 and 0.
 

1. What is a geometry-sequence with unlimited repeated values?

A geometry-sequence with unlimited repeated values is a sequence where the terms have a common ratio, and the ratio is greater than or equal to 1. This means that as the sequence progresses, the terms get larger and larger, without ever reaching a maximum value.

2. How is a geometry-sequence with unlimited repeated values different from a finite geometry-sequence?

A finite geometry-sequence has a limited number of terms and a clearly defined last term, while a geometry-sequence with unlimited repeated values has an infinite number of terms and no defined last term. Additionally, the terms in a finite geometry-sequence do not increase indefinitely like they do in a geometry-sequence with unlimited repeated values.

3. What are some real-life applications of a geometry-sequence with unlimited repeated values?

One example of a real-life application of a geometry-sequence with unlimited repeated values is compound interest in finance. As the interest is compounded over time, the amount of money in the account grows larger and larger, without ever reaching a maximum value. Another example is population growth, where the number of individuals in a population increases exponentially over time.

4. How can you determine the common ratio of a geometry-sequence with unlimited repeated values?

The common ratio of a geometry-sequence with unlimited repeated values can be determined by dividing any term by the previous term. As the sequence progresses, this ratio should remain constant, and it will be greater than or equal to 1.

5. Can a geometry-sequence with unlimited repeated values have a negative common ratio?

No, a geometry-sequence with unlimited repeated values cannot have a negative common ratio. The common ratio must be greater than or equal to 1 in order for the terms to increase indefinitely. A negative common ratio would result in the terms decreasing and eventually reaching 0, which is not characteristic of a geometry-sequence with unlimited repeated values.

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