Digits can repeat: Case 1. 1 letter followed by 3 digits Choose the letter 26 ways. Choose the first digit 10 ways. Choose the second digit 10 ways. Choose the third digit 10 ways. That's 26*10*10*10 = 26000 Case 2. 1 letter followed by 4 digits. Annex a digit to each of the 26000 ways in Case 1. That can be done in 10 ways. That's 26000*10 = 260000 Grand total: 26000 + 260000 = 286000 --------------------------- Digits cannot repeat: Case 1. 1 letter followed by 3 digits Choose the letter 26 ways. Choose the first digit 10 ways. Choose the second digit 9 ways. Choose the third digit 8 ways. That's 26*10*9*8 = 18720 Case 2. 1 letter followed by 4 digits. Annex a fourth digit to each of the 18720 ways in Case 1. That can be done in 7 ways. That's 18720*7 = 131040 Grand total: 18720 + 131040 = 149760 Edwin