Question

The country of Scotstats requires the people in their country to have license tags on their

car such that the first 3 characters are English letters but no letter may repeat. The last 3
characters must each be a number 0 - 9 and again no numbers can be repeated. How
many license tags are possible?

Answer 1

11,232,000

Explanation:

26 choices for the first letter.

25 choices left for the second letter (can't repeat letters)

24 choices left for the third letter

26 x 25 x 24 = 15,600 = possible first 3 characters.

10 choices for the first number

9 choices left for the second number (can't repeat numbers)

8 choices left for the third number

10 x 9 x 8 = 720 = possible last 3 characters.

chatgpt

Answer 2

The licenses have space for 6 characters.

We need to note that there are 26 alphabets and 10 numbers to pick from.

So, for the first character, any of the 26 alphabets can take this spot.

For the second character, 25 alphabets are now available for that space. (Since repetition is not allowed)

For the third character, 24 alphabets are available for that.

For the fourth character, any of the 10 numbers can take up that spot.

For the fifth character, only 9 numbers can take this spot now. (No repetition rule too)

For the sixth character, 8 numbers can take that spot.

So, mathematically, the number of license tags possible will be

`\bold{26 * 25 * 24 * 10 * 9 * 8 = \underline{11,232,000} \ possible \ license \ tags}`