How many different license plates can be made using 3 digits

How many different license plates can be made using 3 digits followed by 3 letters if the first digit must be greater than or equal to 7 and no repetition of letters is allowed?

Solution

there are 26 different letters (a-z) and 10 digits (0-10)

first digit must be greater than or equal to 7(No repetition allowed) = 3

2 letters (No repetition allowed) = ²⁶C₂ =325
2 digits (No repetition is alllwed)= ¹⁰C₂=45
so different license plates can be made = 3 * 325 * 45= 43875