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What is $\binom{10}{0} + \binom{10}{2} + \binom{10}{4} + \binom{10}{6} + \binom{10}{8} + \binom{10}{10}$ ?

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Binomial identities, and proving them by counting twice

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Optiver, Five Rings

What is (100)+(102)+(104)+(106)+(108)+(1010)\binom{10}{0} + \binom{10}{2} + \binom{10}{4} + \binom{10}{6} + \binom{10}{8} + \binom{10}{10}(010​)+(210​)+(410​)+(610​)+(810​)+(1010​)?

More counting and combinatorics questions

What is $\binom{10}{0} + \binom{10}{2} + \binom{10}{4} + \binom{10}{6} + \binom{10}{8} + \binom{10}{10}$ ?