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Question
Roll numbers are created with a letter followed by 3 digits in it, from the letters A, B, C, D and E and any 3 digits from 0 to 9. In how many possible ways can the roll numbers be generated? (except A000, B000, C000, D000 and E000)
Solution
We have a letter followed by 3 digits in the roll number.
The letter is selected from the five letters A, B, C, D, E.
For these 5 letters, we have to select a 3 digit number using the digits 0 to 9.
One's place can be formed using any one of the 10 number 0 to 9 in 10 ways.
Ten's place can be formed in 10 ways.
∴ A two-digit number can be formed in 10 × 10 = 100 ways.
Thousand's place can be formed in 10 ways
∴ A three-digit number can be formed in 10 × 10 × 10 = 1000 ways.
∴ 5 letters can be attached in 5 × 1000 = 5000 ways.
∴ The roll number can be formed in 5000 – 5 = 4995 ways.
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