How many different seven digit phone numbers are available if the only restriction is that the first digit cannot be 0.
9*9*8*7*6*5*4 = 544320 ways
9*10^6
To determine the number of different seven-digit phone numbers available with the restriction that the first digit cannot be 0, we can use the concept of permutations.
Since there are 10 digits (0-9) that can be used to form a seven-digit phone number, we have 10 choices for the first digit.
For the next six digits, we have 10 choices each, as there are no restrictions.
Therefore, the total number of seven-digit phone numbers available is calculated as follows:
Number of choices for the first digit = 10
Number of choices for each of the next 6 digits = 10
Total number of possibilities = 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10^7 = 10,000,000
So, there are 10,000,000 different seven-digit phone numbers available if the only restriction is that the first digit cannot be 0.