Q. 175.0( 2 Votes )

A biologist study

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 . 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


= 369600


Hence, total number of permutation of given 12 molecules will be equals to 369600.


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