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# How many different signals can be made from 4 red, 2 white, and 3 green flags by arranging all of them vertically on a flagstaff?

Given, the flags: Red, White, and Green. Total of 9 flags and it has 3 repeated flags Green, Red, and White. The flag Green is repeated thrice, and flag Red is repeated 4 times, flag White is repeated twice.

To find: Number of ways of arranging the flags vertically on a flagstaff.

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

= 1260

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

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