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Question
If C0 + C1 + C2 + ... + Cn = 256, then 2nC2 is equal to
Options
56
120
28
91
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Solution
120
If set \[S\] has n elements, then
\[ \Rightarrow 2^n = 2^8 \]
\[ \Rightarrow n = 8\]
\[ \Rightarrow^{16} C_2 = \frac{16!}{2! 14!} = \frac{16 \times 15}{2} = 120\]
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