Administration section of a university has started to create roll numbers for the students, following the format ‘23Z170’ using the digits 0, 1, 2, 3, 4, 5, 6, and a capital letter at the third position. Assume no digits are repeated. Find the number of ways in which the administration section can create a unique roll number65,52052,92056,16046,800
Question
Administration section of a university has started to create roll numbers for the students, following the format ‘23Z170’ using the digits 0, 1, 2, 3, 4, 5, 6, and a capital letter at the third position. Assume no digits are repeated. Find the number of ways in which the administration section can create a unique roll number65,52052,92056,16046,800
Solution
The roll number format is '23Z170', where Z is a capital letter and the digits are not repeated.
Step 1: Determine the number of options for each position.
- For the first position, we have 8 options (0, 1, 2, 3, 4, 5, 6, 7).
- For the second position, we have 7 remaining options (since no digit is repeated).
- For the third position, we have 26 options (A-Z).
- For the fourth position, we have 6 remaining options (since no digit is repeated).
- For the fifth position, we have 5 remaining options (since no digit is repeated).
- For the sixth position, we have 4 remaining options (since no digit is repeated).
Step 2: Calculate the total number of ways.
The total number of ways is the product of the number of options for each position.
So, the total number of ways = 8 * 7 * 26 * 6 * 5 * 4 = 65,520 ways.
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