18. Linear time algorithm for the Selection problem, (the computational problem to find the kth largest number among n numbers):

(a) Typical implementation is to divide the n numbers into $\lceil n/5 \rceil$ groups. We then find the medians of the $\lceil n/5 \rceil$ groups, and then find the median of those medians. After $(\Theta(n) + T(\lceil n/5 \rceil))$ time, we can drop a set S of numbers because S does not contain the answer. Show that $|S| \ge n/4$ where |S| is the size of S. (4%).

(b) Can we divide the n numbers into $\lceil n/7 \rceil$ groups instead of $\lceil n/5 \rceil$ groups? Why or why not? (5%).