40. 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)?