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 initial A (for Adenine), C (for Cytosine), C (for Guanine) and T (for Thymine) and 3 molecules of each kind. How many different such arrangements are possible?

Answer 1

Total number of molecules = 12
Now,
the chain contains 4 different molecules A, c, g and T, and 3 molecules of each kind,
$\therefore$ the number of different arrangements

= $\frac{12!}{3131313!}$

= $\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3!}{3\times 2\times 3\times 2\times 3\times 2\times 3!}$

= 369600

Hence, the number of different possible arrangements are = 369600.