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23 people shake hands how many hand shaking r possible if thety r in pair of cyclic sequence

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.it is dark bedroom n i want to get 2 socks of sme color which contain 24 red n 24 blue .how mnay socks do i havve to take to get atleast 2 socks of same color .10 men,10 women dance wid each other find d possibilty that 2 men r dancing with sme women n vice versa