A person wants to invite one or more of his friend for a dinner party. In how many ways can he do so if he has eight friends :-

2^{8}

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2^{8} - 1

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8^{2}

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^{8} C_{1} +^{8} C_{2} + . . . . . +^{8} C_{8}

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Solution

The correct options are
A $2^{8} - 1$
D $^{8} C_{1} +^{8} C_{2} + . . . . . +^{8} C_{8}$
Selection of atleast $8$ people will be
$=^{8} C_{1} +^{8} C_{2} + . . .^{8} C_{8}$
$= \sum_{r = 1}^{8}^{8} C_{r}$
$= (1 + x)^{8} -^{8} C_{0}$ at $x = 1$
$= 2^{8} - 1$ .

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