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ABCD is a quadrilateral and P , Q are mid-points of CD, AB respectively. Let AP , DQ meet
at X, and BP , CQ meet at Y . Prove that
area of ADX + area of BCY = area of quadrilateral PXQY

1. The number of ways in which three non-negative integers $$n_1, n_2, n_3$$ can be chosen such that $$n_1+n_2+n_3 = 10$$ is
(A) 66 (B) 55 (C) $$10^3$$ (D) $$\dfrac {10!}{3!2!1!}$$