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  4. Median of 2nC0, 2nC1, 2nC2, 2nC3, ldots, 2nCn (where n is even) is

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Q. Median of $ ^{2n}C_{0}, ^{2n}C_{1}, ^{2n}C_{2}, ^{2n}C_{3}, \ldots, ^{2n}C_{n} $ (where $ n $ is even) is

UPSEEUPSEE 2008

Solution:

${ }^{2 n} C_{0},{ }^{2 n} C_{1},{ }^{2 n} C_{2}, \ldots,{ }^{2 n} C_{n}$ is odd number of binomial coefficients (when $n$ is even) and middle binomial coefficient is ${ }^{2 n} C_{n / 2}$ which is required median.