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${ }^{10} C_1+{ }^{10} C_3+{ }^{10} C_5+{ }^{10} C_7+{ }^{10} C_9=$
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Verified Answer
The correct answer is:
$2^9$
We know that
$2^{n-1}={ }^n C_0+{ }^n C_2+{ }^n C_4+\ldots .={ }^n C_1+{ }^n C_3+{ }^n C_5+\ldots . .$
So, ${ }^{10} C_1+{ }^{10} C_3+{ }^{10} C_5+\ldots . .+{ }^{10} C_9=2^{10-1}=2^9$
$2^{n-1}={ }^n C_0+{ }^n C_2+{ }^n C_4+\ldots .={ }^n C_1+{ }^n C_3+{ }^n C_5+\ldots . .$
So, ${ }^{10} C_1+{ }^{10} C_3+{ }^{10} C_5+\ldots . .+{ }^{10} C_9=2^{10-1}=2^9$
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