(a) Which is larger:

(b) For a fixed n, consider (n k) as a function of k. Figure out for which k it is increasing and for which it is decreasing. Where does it attain its maximal value for an even n, for an odd n? In what sense is the picture symmetric? (Advice: Compare the values for k and k + 1.)

(c) If you toss a coin 100 times, which is more likely: getting 50 heads or 49 heads; 50 heads or 51 heads; 49 heads or 51 heads; 41 heads or 59 tails?