Probability Review , How many different numbers can you make with the digits 2,3,and 4 if you can use each digit as many times as you want?
an infinite number. Start with
22222222222222222222222222222. . .
To find out how many different numbers can be made using the digits 2, 3, and 4, where each digit can be used as many times as you want, we need to consider the total number of possibilities for each digit position.
Since we can use each digit (2, 3, and 4) an unlimited number of times, the number of possibilities for each digit position is 3. This is because we have three choices for each position - 2, 3, or 4.
In this case, the total number of different numbers we can make would be the product of the number of possibilities for each digit position. Since there are 3 digit positions (ones, tens, and hundreds), we multiply 3 three times.
So, the total number of different numbers that can be made using the digits 2, 3, and 4, with each digit used as many times as you want, is 3^3, which equals 27.