Use Pigeonhole Principle to show: a) Among any 11 integers, at least two must have the same last digit. b) Let s,,s2..,S101 be 101 bit strings of length at most 9. Prove that there exist two strings, si and 9, where i # j, that contain the same number of 0's and the same number of 1's. (For example, strings 001001 and 101000 contain the same number of O's and the same number of I's.) Use Pigeonhole Principle to show: a) Among any 11 integers, at least two must have the same last digit. b) Let s,,s2..,S101 be 101 bit strings of length at most 9. Prove that there exist two strings, si and 9, where i # j, that contain the same number of 0's and the same number of 1's. (For example, strings 001001 and 101000 contain the same number of O's and the same number of I's.)