Question

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.

How many such chain molecules are there? |Hint: If the three A's were distinguishable from one another- A A-and the 5's, Cs, 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?] chain molecules.

Answer 1

There are 12!/((3!)^4) chain molecules.

Step-by-step explanation:

To find the number of chain molecules, we can treat the three molecules of each type as identical. If we ignore the subscripts, there would be 3! (3 factorial) ways to arrange the 12 molecules. However, since there are three identical molecules of each type, we need to divide by 3! for each type to account for the repetitions. Therefore, the number of chain molecules is 12!/((3!)^4).