SOLUTION: There is a problem I don't understand. example: The first year the state of Pennsylvania issued railroad memorial license plates, the plates had a picture of a stream engine

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Question 1111274: There is a problem I don't understand.
example:
The first year the state of Pennsylvania issued railroad memorial license plates, the plates had a picture of a stream engine followed by four digits. Assuming that repetitions are allowed, how many railroad memorial plates could be issued.
the solution has four "10s" that equal 10,000and I don't understand how they got that answer. how did they come up with the number 10. I just need someone to shed some light on this for me.
Tia
Found 2 solutions by ikleyn, amalm06:
Answer by ikleyn(52834)   (Show Source): You can put this solution on YOUR website!
.
The digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 - in all, there are 10 digits.


Any of 10 digit can be placed on the most-left position.  It gives 10 options.

Any of 10 digit can be placed on the next      position.  It gives 10 options.

Any of 10 digit can be placed on the third     position.  It gives 10 options.

Any of 10 digit can be placed on the fourth    position.  It gives 10 options.


All these options are INDEPENDENT. You can combine them in ANY way.


Therefore, there are   possible combinations of 10 digits in 4-digit words.

It is the explanation you wanted.

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It is THE STANDARD explanation/solution for such problems.


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By the way, this fact is STRICTLY PARALLEL to the fact that there are integer numbers from 0 = 0000 to 9999 inclusively.


Answer by amalm06(224)   (Show Source): You can put this solution on YOUR website!
There are 4 independent events and each event can occur in 10 possible ways. Since the events are independent, you multiply them to find the total number of possible combinations.
You can pick the first digit 10 different ways, the 2nd digit 10 different ways, the third digit 10 different ways, and the 4th digit 10 different ways.
So there are 10*10*10*10=10000 possible ways to pick the digits (Answer).
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