# How many different 5 digit numbers license plates can be made if First digit cannot be zero and the repetition of digits is not allowed?

Answer

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**Hint:**To obtain how many 5 digit numbers license plates we can obtain under given conditions we have to fill five places. The ones, tens, hundredth, thousandth and ten-thousandth place. Firstly we will find the number of possible ways each place can be filled then we will multiply all the possible choices and get our desired answer.

**Complete step-by-step solution:**

We have to obtain a 5 digit number license plate such that the first digit cannot be zero and the repetition of digits is not allowed.

As we know we have 10 choices in total for each place in a 5 digit number license plate.

As the first digit can’t be 0 so we are left with 9 choices for the one place.

Then for tens of places we are left with 9 choices as numbers can’t be repeated.

Then for the hundredth place we will have 8 choices as two numbers are already used.

Then for the thousandth place we will have 7 choices as three numbers are already used.

Then for ten-thousandth place we will have 6 choices as four numbers are already used.

So from all the five statement above we get the following outcome:

Total number of 5 digit number license plate =$9\times 9\times 8\times 7\times 6 =27216$

**Hence a total of 27216 different 5 digit number license plates can be made if First digit cannot be zero and the repetition of digits is not allowed.**

**Note:**The concept used in such problems is to get the possible choices for each place by keeping the given condition in mind and then find the product of all the choices. As repetition is not allowed so the choices as we move forward keeps on decreasing.

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