How many 4 digit number in base A system?

In a base ( A ) numbering system, the total number of 4-digit numbers can be calculated by considering that the first digit (most significant) cannot be zero. Therefore, for the first digit, there are ( A - 1 ) options (from 1 to ( A - 1 )), and for each of the remaining three digits, there are ( A ) options (from 0 to ( A - 1 )). Thus, the total number of 4-digit numbers in base ( A ) is given by the formula: ((A - 1) \times A^3).