Description
How many nine-digit student identification numbers can be created from letters and numbers if the first four characters must be upper case letters from A to D and the last five must be digits from 0 to 9? Repetition of letters and numbers is not allowed.
Explanation & Answer
The first letter can be A,B, C or D .. 4 choices
For the second letter you have 3 choices because no repetition is allowed
For the third letter you have 2 choices because the previous 2 letters cannot be repeated
For the fourth letter there is only 1 choice
Hence , since the order is important, you have 4! = 4 x 3 x 2 x1 = 24 different permutations
For the first number you have 10 choices (any digit from 0 to 9)
For the second number you have 9 choices because no repetition is allowed
For the third number you have 8 choices because no repetition is allowed
For the fourth number you have 7 choices because no repetition is allowed
For the fifth number you have 6 choices because no repetition is allowed
Hence the permutation of 5 numbers can occur in 10 x 9 x 8 x 7 x 6 = 30240
Finally, the letters and numbers together can be chosen in
24 x 30240 = 725760 ways
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