prove-that-C-n-o-C-n-p-C-n-1-C-n-1-p-1-C-n-p-C-n-p-0-2-p-C-n-p-

Question Number 31046 by abdo imad last updated on 02/Mar/18

$${prove}\:{that}\:{C}_{{n}} ^{{o}} \:{C}_{{n}} ^{{p}} \:+{C}_{{n}} ^{\mathrm{1}} \:{C}_{{n}−\mathrm{1}} ^{{p}−\mathrm{1}} \:+…{C}_{{n}} ^{{p}} \:{C}_{{n}−{p}} ^{\mathrm{0}} =\mathrm{2}^{{p}} \:{C}_{{n}} ^{{p}} \:\:\:. \\ $$

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