Discrete Math-No other information was given

3. Argue whether or not there must be two people in Chicago who have social security numbers with the same last four digits. Give your sources for relevant numbers and facts to support your argument and explain any necessary calculations.

4.

(a) How many hexadecimal numbers from 1 through FFF do not have any repeated digits?

(b) How many hexadecimal numbers from 1 through FFF have at least one repeated digit?

(c) What is the probability that a hexadecimal number chosen at random from 1 through FFF has at least one repeated digit?

5. How many integers from 1000 through 9999 must you pick in order to be sure that at least two of them have a digit in common? (For example, 2493 and 1538 have the digit 3 in common.) Explain your reasoning.

6. Recall that a bit string is a string of 0's and 1's.

(a) How many bit strings have length 12?

(b) How many bit strings of length 12 have exactly 6 0's?

(c) What is the probability that a bit string of length 12 has exactly 6 0's?

(d) How many bit strings of length 12 have at least 9 0's?