Imagine a fictional scenario where a new area code 424 has just been as- signed to Milwaukee. To request a phone number with this new area code, a com- puter program selects a 7-digit number 51525354555657 randomly. That is, for i = 1,...,7, a random number generator picks a number from 0 to 9 and assigns it to sį. Thus, the program can potentially output 000-0000 as a phone number.
a. How many possible phone numbers do not contain the numbers 0 and 1 (e.g. 227-5986)?
b. How many possible phone numbers contain 2021 as a contiguous subsequence (e.g. 532-0219 or 202-1667 but not 230-6179 nor 227-5986)? 1
c. How many possible phone numbers makes use of at least two numbers (e.g. 229- 5170 but not 777-7777)?
d. How many possible phone numbers contain exactly three 3's? e. How many possible phone numbers contain at least five 3's?