Q. 185.0( 1 Vote )

In how many ways can 4 red, 3 yellow and 2 green discs be arranged in a row if the discs of the same color are indistinguishable?

Answer :

Given, the disc: Red, Yellow, and Green. Total of 9 discs and it has 3 repeated discs Green, Red, and Yellow. The disc Green is repeated twice, and disc Red is repeated 4 times, disc Yellow is repeated thrice.

To find: Number of the arrangement of discs.


The problem can now be rephrased as to find total number of permutations of 9 objects (R, R, R, R, Y, Y, Y, G, G) of which three objects are of same type (Y, Y, Y), and two objects are of another type (G, G), and 4 objects are of different type (R, R, R, R).


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.


Total number of such permutations will be


=


= 1260


Hence, total number of permutations of the given type is 1260.


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