Counting Principles - Combinations and Permutations

Mathematics
Tutor: None Selected Time limit: 1 Day

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.

May 21st, 2015

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


May 21st, 2015

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