According to a​ survey, 61​% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly​ selected, and the number cleared by arrest or exceptional means is recorded.
​(a) Find the probability that exactly 39 of the murders were cleared.
​(b) Find the probability that between 36 and 38 of the​ murders, inclusive, were cleared.
​(c) Would it be unusual if fewer than 20 of the murders were​ cleared? Why or why​ not?