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Permutations — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPermutations4 Marks
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?
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Answer

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 $=\frac{12!}{3!\ 3!\ 3!\ 3!}$ $=\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3!}{3\times2\times3\times2\times3\times2\times3!}$ $=369600.$ Hence, the number of different possible arrangements are = 369600.

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