MathDB
2018 Individual #21

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January 13, 2023
2018 Individual

Problem Statement

Find the sum: 11×(20)+10×(31)+9×(42)+⋯+2×(119)+(1210)11 \times \dbinom20 + 10 \times \dbinom31 + 9 \times \dbinom42 + \cdots + 2 \times \dbinom{11}9 + \dbinom{12}{10} Where (nr)\tbinom{n}{r} is combination function given by n!r!(n−r)!\tfrac{n!}{r!(n-r)!}
<spanclass=′latex−bold′>(A)</span>351<spanclass=′latex−bold′>(B)</span>841<spanclass=′latex−bold′>(C)</span>901<spanclass=′latex−bold′>(D)</span>991<spanclass=′latex−bold′>(E)</span>1001<span class='latex-bold'>(A) </span> 351\qquad<span class='latex-bold'>(B) </span> 841\qquad<span class='latex-bold'>(C) </span> 901\qquad<span class='latex-bold'>(D) </span> 991\qquad<span class='latex-bold'>(E) </span> 1001
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