Question

A biologist studying the genetic code is interested to know the number of possible arrangements of 12 molecules in a chain. The chain contains 4 different molecules represented by the initials A (for Adenine), C (for Cytosine), G (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?

Answer 1

Number of molecules in a chain = 12
Number of molecules with initials A = 3
Number of molecules with initials C = 3
Number of molecules with initials G = 3
Number of molecules with initials T = 3
Thus, total arrangements of all the molecules in the chain = Number of arrangements of 12 things of which 3 are similar to the first kind, 3 are similar to the second kind, 3 are similar to the third kind and 3 are similar to the fourth kind
= $\frac{12!}{3!3!3!3!}$ = 369600