Question

Roll numbers are created with a letter followed by 3 digits in it. From the letter A, B, C, D, E and any 3 digits from 0 to 9. Then, in how many possible ways can the roll numbers be generated?
$\left[2\right]$

Answer 1

We have a letter followed by 3 digits in the roll number.
The letter is selected from A, B, C, D, E.
For these 5 letters we have to select a 3 digit number using the digits 0 to 9.
Once place can be formed using any one of the 10 numbers, 0 to 9 in 10 ways.
Tens place can be formed in 10 ways.
$\left[1\right]$
∴ A two digit number can be formed in 10 × 10 = 100 ways.
Thousands place can be formed in 10 ways
∴ A 3 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 ways.
$\left[1\right]$