if a 6-digit lottery ticket is sold and includes all possible digits from 0 to 9, then how many different tickets could be sold, if the order in which you pick the numbers matters?

1 answer

To determine how many different 6-digit lottery tickets can be sold using the digits from 0 to 9, where the order of the digits matters and each digit can be used multiple times, we can analyze the situation as follows:

  1. Each of the 6 digit positions in the lottery ticket can be filled by any one of the 10 digits (0 through 9).
  2. Since the digits can be repeated and the order matters, we have 10 choices for each of the 6 positions.

Thus, the total number of different 6-digit tickets can be calculated using the formula for the number of combinations with repetition allowed:

\[ \text{Total tickets} = 10^6 \]

Calculating that,

\[ 10^6 = 1,000,000 \]

Therefore, the total number of different 6-digit lottery tickets that could be sold is \( \boxed{1000000} \).