^{15}C_3 + ^{15}C_5 + ldots + ^{15}C_{15} = ? | vedclass

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(B) We know that the sum of binomial coefficients with odd indices is given by: $^{n}C_1 + ^{n}C_3 + ^{n}C_5 + \ldots = 2^{n-1}$. For $n = 15$, we hav

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$2^{14} - 15$

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(B) We know that the sum of binomial coefficients with odd indices is given by: $^{n}C_1 + ^{n}C_3 + ^{n}C_5 + \ldots = 2^{n-1}$. For $n = 15$, we have: $^{15}C_1 + ^{15}C_3 + ^{15}C_5 + \ldots + ^{15}C_{15} = 2^{15-1} = 2^{14}$. We need to find the sum $^{15}C_3 + ^{15}C_5 + \ldots + ^{15}C_{15}$. This is equal to $2^{14} - ^{15}C_1$. Since $^{15}C_1 = 15$, the sum is $2^{14} - 15$.

$^{15}C_3 + ^{15}C_5 + \ldots + ^{15}C_{15} = ?$

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