2. Use the pigeonhole principle for the following questions. (a) You randomly select k integers between 1 and 100, inclusive. What is the smallest k that guarantees that at least one pair of the selected integers will sum to 101? Prove your answer. (b) Prove that among a group of 621 people, there are at least 21 who are born on the same day of the month (e.g., the 21st or the 12th, etc.). Is the same fact true if there are only 620 people