Each student has an ID number consisting of 5 digits ( the first digit is non-zero, and digits can be repeated) followed by letters A,B,C,and D (letters cannot be repeated). How many different student numbers are possible?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Each student has an ID number consisting of 5 digits ( the first digit is non-zero, and digits can be repeated) followed by letters A,B,C,and D (letters cannot be repeated). How many different student numbers are possible?
Number of digits in the ID number = 5
Since first digit is non-zero, the number of possibilities for first digit = 9
The remaining 4 places can be filled by any of the 10 digits (since they can be repeated and can be zero)
Therefore, number of possibilities for remaining 4 digits =
Now, number of letters in the ID = 4
Therefore,
Number of ways in which the first letter can be selected = 4
Since letters cannot be repeated, number of ways in which the second letter can be selected = 3
Number of ways in which the third letter can be selected = 2
And lastly, number of ways in which the fourth letter can be selected = 1
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