Evaluate each of the following without directly expanding factorials

MATHEMATICS · Subjective · CBSE · Mathematics · Binomial Theorem · Binomial Theorem

Problem

Evaluate each of the following without directly expanding factorials. (a) 12C4+12C5{}^{12}C_{4}+{}^{12}C_{5} (b) 9C3+9C4{}^{9}C_{3}+{}^{9}C_{4} (c) Hence, or otherwise, find 15C7+15C8{}^{15}C_{7}+{}^{15}C_{8}.

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