# John wants to form 5 digit numbers from the set of integers from 0 to 9 inclusive. Assuming he can reuse numbers, and the 5 digit number must start with and 8 and end with a 0, how many different numbers may he form?

Apr 1, 2017

$1000$ possibilities

#### Explanation:

The first number must be an $8$, so there is only $1$ possibility for the first digit.
The second number can be anywhere between $0$ to $9$, so there are $10$ possibilities for the second digit.
The third number can be anywhere between $0$ to $9$, so there are $10$ possibilities for the second digit.
The fourth number can be anywhere between $0$ to $9$, so there are $10$ possibilities for the second digit.
The fifth number must be a $0$, so there is only $1$ possibility for the last digit.

We multiply these possibilities to get $1 \cdot 10 \cdot 10 \cdot 10 \cdot 1 = 1000$ possibilities.