A) \[\frac{{{2}^{50}}}{51}\]
B) (b) \[\frac{{{2}^{50}}-1}{51}\]
C) \[\frac{{{2}^{50}}-1}{50}\]
D) None of these
Correct Answer: A
Solution :
\[\left( \,\frac{^{50}{{C}_{0}}}{1}+\frac{^{50}{{C}_{2}}}{3}+......+\frac{^{50}{{C}_{50}}}{51} \right)\] \[=\left( \frac{1}{1}+\frac{50\times 49}{3\times 2!}+....+\frac{1}{51} \right)\] \[=\frac{1}{51}\left( \frac{51}{1!}+\frac{51\times 50\times 49}{3!}+.....+1 \right)\]\[=\frac{1}{51}({{\,}^{51}}{{C}_{1}}{{+}^{51}}{{C}_{3}}+...{{+}^{51}}{{C}_{51}})\] \[=\frac{1}{51}{{2}^{51-1}}=\frac{{{2}^{50}}}{51}\]
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