Automobile License Plate An automobile license plate consists of 3 letters followed by 4 digits. How many different plates can be made if repetitions are allowed? If repetitions are not allowed? If repetitions are allowed in the letters but not in the digits? (4–4)

Solution 27RE

Step1 of 4:

The number of letters consists an automobile license plate = 3. And it is followed by 4 digits.

Here our goal is:

a). We need to check how many different plates can be made. When repetitions are allowed.

b). We need to check how many different plates can be made. When repetitions are not allowed.

c). We need to check how many different plates can be made. When repetitions are allowed in the letters but not in the digits.

Step2 of 4:

a).

The number of letters in english language = 26. So, with repetitions there can be:

Digits 0 through 9 are allowed. So, with repetitions there can be:

When repetitions are allowed then,

Therefore, There are 175760000 different plates can be made.

Step3 of 4:

b).

Suppose repetitions are not allowed. The first letter is 1 of 26, 1 of 25, 1 of 25. Then,...