$(^{7} C_{0} +^{7} C_{1}) + (^{7} C_{2} +^{7} C_{3}) + .... + (^{7} C_{6} +^{7} C_{7}) =$

2^{8} - 2

2^{7} - 1

2^{7}

2^{8} - 1

2^{7} - 2

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(^{7} C_{0} +^{7} C_{1}) + (^{7} C_{2} +^{7} C_{3}) + .... + (^{7} C_{6} +^{7} C_{7}) =

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Text solutionVerified

(^{7} C_{0} +^{7} C_{1}) + (^{7} C_{2} +^{7} C_{3}) + - - - - - - + (^{7} C_{6} +^{7} C_{7})

=^{7} C_{0} +^{7} C_{1} + - - - - +^{7} C_{7}

= 2^{7} [∵ C_{0} + C_{1} + C_{2} + - - - - + C_{n} = 2^{n}]

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