InterviewSolution
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InterviewSolution
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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 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» Given, The molecules’ initials A, G, T, and C (All are repeated thrice). AAAGGGTTTCCC To find : Number of arrangements of these 12 molecules in such a way that all arrangements must be distinct. The problem can now be rephrased as to find a number of permutations of 12 objects in which 3 objects are of one type, 3 objects are of another type, 3 objects are of a third type, and remaining 3 objects are of different type. Since we know, Permutation of n objects taking r at a time is nPr,and permutation of n objects taking all at a time is n! And, We also know, Permutation of n objects taking all at a time having p objects of the same type, q objects of another type, r objects of another type is \(\frac{n!}{p!\times q!\times r!}\). i.e., The number of repeated objects of same type are in denominator multiplication with factorial. The number of permutation of 12 objects with repeating molecules in the factor of 3 = \(\frac{12!}{3!\times 3!\times 3!\times 3!}\) = 369600 Hence, Total number of permutation of given 12 molecules will be equals to 369600. |
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