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# counting in two ways… find bijection

Home Forums Math Olympiad, I.S.I., C.M.I. Entrance Combinatorics counting in two ways… find bijection

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Aritra
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#24710

swastik pramanik
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Notice that $$|A\times B|=mn$$. Also, $$|C_i|=n$$ for all $$i=1,2,3,\cdots ,m$$. hence $$\sum_{i=1}^m |C_i|=\sum_{i=1}^m n=mn$$. Similarly, we can prove that $$\sum_{j=1}^n |D_j|=mn$$.

And hence, we get our desired result.

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