To solve this problem it is helpful to consider which numbers can be placed in which of the seven digit spots. So, the last three digit places for the phone number each only have 1 option because they have to be 3, 0, and 9 consecutively. Thus, if all the numbers in the seven digit phone number need to be distinct, then there are 7 numbers left to consider for the first digit (1, 2, 4, 5, 6, 7, 8). So, for the first digit we have 7 options remaining and for the second digit we will only have 6 options left because now one number was chosen for the first digit so we must exclude it when choosing the second digit. This pattern will continue so that the options available for the third and fourth digits are 5 and 4, respectively. So we know that there are 7*6*5*4*1*1*1 = 840 ways that we can produce a phone number with the stated qualifications. To produce the probability that we have a phone number like this we need to divide 840 by the total number of phone numbers that can be produced. The total number of phone numbers will be 10^7 = 10,000,000 because each digit in the phone number can be any of 10 numbers 0 through 9. So the probability will be 840/10^7 = 0.000084.
