The value of
$(^{7} C_{0} +^{7} C_{1}) + (^{7} C_{1} +^{7} C_{2}) + . . . . + (^{7} C_{6} +^{7} C_{7})$ is

2^{8} - 2

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2^{8} - 1

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2^{8} + 1

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2^{8}

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Solution

The correct option is C $2^{8} - 2$
$= (^{7} C_{0} +^{7} C_{1}) + (^{7} C_{1} +^{7} C_{2}) + . . . . + (^{7} C_{6} +^{7} C_{7})$
$=^{8} C_{1} +^{8} C_{2} + . . . . . +^{8} C_{7}$
$= (^{8} C_{0} +^{8} C_{1} + . . . . . +^{8} C_{7} +^{8} C_{8}) -^{8} C_{0} -^{8} C_{8}$
$= 2^{8} - 1 - 1 = 2^{8} - 2$

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Similar questions

The value of $(^{7} C_{0} +^{7} C_{1}) + (^{7} C_{1} +^{7} C_{2}) + . . . + (^{7} C_{6} +^{7} C_{7})$

{(\frac{1 + i}{\sqrt{2}})}^{8} + {(\frac{1 - i}{\sqrt{2}})}^{8}

{(\frac{1 + i}{\sqrt{2}})}^{8} + {(\frac{1 - i}{\sqrt{2}})}^{8}

28 - \frac{1}{[28 {28 - (28 - 28 + 28)}]}

(\frac{1 + i}{\sqrt{2}})^{8} + (\frac{1 - i}{\sqrt{2}})^{8} = 2

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