42. Three molecules of type A, three of type B, three of type C, and three of type D are to be linked together to form a chain molecule. One such chain molecule is ABCDABCDABCD, and another is BCDDAAABDBCC.

a. How many such chain molecules are there?
(Hint: If the three A s were distinguishable from one another A1, A2, A3 and the B s, C s, and D s were also, how many molecules would there be? How is this number reduced when the subscripts are removed from the A s?)

b. Suppose a chain molecule of the type described is randomly selected. What is the probability that all three molecules of each type end up next to one another (such as in BBBAAADDDCCC)?