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

Question

Median of 2nC0, 2nC1, 2nC2, 2nC3, ldots, 2nCn (where n is even) is (A)  2nC(n/2)  (B)  2nC(n+1/2)  (C)  2nC(n-1/2)  (D) None of these

Tardigrade Admin · Accepted Answer

2 n C0, 2 n C1, 2 n C2, ldots, 2 n Cn is odd number of binomial coefficients (when n is even) and middle binomial coefficient is 2 n Cn / 2 which is required median.

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

$^{2 n} C_{\frac{n}{2}}$

$^{2 n} C_{\frac{n + 1}{2}}$

$^{2 n} C_{\frac{n - 1}{2}}$

None of these

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

Q. Median of 2nC0​,2nC1​,2nC2​,2nC3​,…,2nCn​ (where n is even) is

2nC2n​​

2nC2n+1​​

2nC2n−1​​