A) \[\frac{5}{17}\]
B) \[\frac{4}{17}\]
C) \[\frac{5}{16}\]
D) \[\frac{5}{18}\]
Correct Answer: D
Solution :
In out of 9 tickets, 5 tickets are odd numbers and 4 tickets are even number. Required probability\[=\left\{ \frac{{{\,}^{5}}{{C}_{1}}}{{{\,}^{9}}{{C}_{1}}} \right.\times \frac{{{\,}^{4}}{{C}_{1}}}{{{\,}^{8}}{{C}_{1}}}\times \frac{{{\,}^{4}}{{C}_{1}}}{{{\,}^{7}}{{C}_{1}}}\] \[\left. +\frac{{{\,}^{4}}{{C}_{1}}}{{{\,}^{9}}{{C}_{1}}}\times \frac{{{\,}^{5}}{{C}_{1}}}{{{\,}^{8}}{{C}_{1}}}\times \frac{{{\,}^{3}}{{C}_{1}}}{{{\,}^{7}}{{C}_{1}}} \right\}\] \[=\frac{5}{9}\times \frac{4}{8}\times \frac{4}{7}+\frac{4}{9}\times \frac{5}{8}\times \frac{3}{7}\] \[=\frac{80+60}{504}=\frac{140}{504}\] \[=\frac{5}{18}\]
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