question_answer

\[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{50}}\] are fifty real numbers such that \[{{x}_{r}}<{{x}_{r+1}}\] for \[r=1,2,3....49.\] Five numbers out of these are picked up at random. The probability that the numbers have \[{{x}_{20}}\] as the middle numbers, is

A) \[\frac{^{20}{{C}_{2}}{{\times }^{30}}{{C}_{2}}}{^{50}{{C}_{5}}}\]

B) \[\frac{^{30}{{C}_{2}}{{\times }^{19}}{{C}_{2}}}{^{50}{{C}_{5}}}\]

C) \[\frac{^{19}{{C}_{2}}{{\times }^{31}}{{C}_{2}}}{^{50}{{C}_{5}}}\]

D) None of these