Question

Employees hired to work at Z incorporated are all assigned an identification code . Each code consists of 2 letters , followed by 3 digits, and then 1 letter : BW 204 -for example . The first letter MUST be an A, Bor C. How many codes are possible if: Both letters and numbers may not repeat ?

Answer 1

Here' the answer to the question. Please write back in case you've doubts.

Code: 2 letters, followed by 3 digits, and then 1 letter (_ _) ( _ _ _)( _)

1. First letter is either of A, B or C = 3

2. The second letter can be any of the 25 remaining letters.

3. The 3 digits can be filled in 10*9*8 = 720 ways.

( there are 10 digits 0 to 9, when of them is chosen, 9 are left, and then after 1 more selection 8 remain)

4. The last space can be filled by a letter, which can be filled in 24 ways ( 25-1 = 24 ways)

So, total ways this can be done = 3*25*720*24 = 1296000 ways