License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?
26 * 26 * 26 * 10 * 10 * 10 = ?
Show all work. Mary purchased a package of 11 different plants, but she only needed 8 plants for planting. In how many ways can she select the 8 plants from the package to be planted?
To determine the number of possible license plates that can be made with 3 letters followed by 3 digits, we need to calculate the number of possibilities for each segment and then multiply them together.
First, let's determine the number of possibilities for the letter segment. Since repetition is allowed, there are 26 options for each of the 3 letters (A-Z). So, the total number of possibilities for the letter segment is 26^3.
Next, let's calculate the number of possibilities for the digit segment. Similar to the letters, repetition is allowed, and there are 10 options for each of the 3 digits (0-9). So, the total number of possibilities for the digit segment is 10^3.
Now, to get the total number of possible license plates, we multiply the number of possibilities for the letter segment by the number of possibilities for the digit segment:
26^3 * 10^3 = 17,576,000
Therefore, there can be a total of 17,576,000 possible license plates if repetition of letters and digits is allowed.