how many different license plates can be made consisting of three letters by four digits?
3^4 = 81
I thought order matters in this problem because it says 3 letters then 4 digits.
So should nPr be used?
26P3= 15600
10P4 = 5040
(5040)(15600)= 78624000
To find out the number of different license plates that can be made consisting of three letters followed by four digits, we need to determine the number of possibilities for each position and then multiply them together.
1. Letters: There are 26 letters in the English alphabet (assuming no special characters or accents are allowed). Since there are three positions for letters, the number of possibilities is 26 raised to the power of 3, which is 26 * 26 * 26 = 17,576.
2. Digits: There are 10 digits (0-9) available for each of the four digit positions. So, the number of possibilities for the digits is 10 raised to the power of 4, which is 10 * 10 * 10 * 10 = 10,000.
Now, multiply the number of possibilities for the letters by the number of possibilities for the digits: 17,576 * 10,000 = 175,760,000.
Therefore, there can be 175,760,000 different license plates consisting of three letters followed by four digits.