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

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    .

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

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