Q2. a. How many strings (considering only lowercase alphabets) are there of length five or less that begin and end with the alphabet "a"? (Do not consider empty string). Q2. b. Suppose that a software company has 7 front-end developers and 9 back-end developers. A standard team is formed by having at least one front-end developer and at least one back-end developer. How many ways are there to form a standard team of seven members so that it must have more front-end developers than back-end developers? Q2. c. In a game of UNO, there are cards of 4 colors- red, green, blue and yellow. There are 25 cards for each color (there are some special cards, but we will not be considering them now). A player is dealt 7 cards in a round. Now using the pigeonhole or generic pigeonhole principle do the followings: i. Explain why there is no guarantee that a player will get at least 2 blue cards. ii. Minimum how many cards should be picked to ensure that he gets at least 3 cards of the same color