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Let there be 3 red, 2 yellow and 2 green signal flags. How many different signals are possible if we wish to make signals by arranging all of them vertically on a staff?

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#### Solution

We have to arrange totally 7 flags out of which 3 are one kind (Red) 2 are of another kind (yellow) and 2 are of third kind (green)

So, total number of signals = `(7!)/(3! 2! 2!)`

`= (7 xx 6 xx 5 xx 4 xx 3!)/(3! xx 2 xx 2)`

= 7 × 6 × 5 = 210

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