A) \[\frac{41}{161}\]
B) \[\frac{120}{161}\]
C) \[\frac{21}{161}\]
D) None of these
Correct Answer: A
Solution :
Total number of ways of selecting 4 socks \[{{=}^{24}}{{C}_{1}}{{\times }^{23}}{{C}_{1}}{{\times }^{22}}{{C}_{1}}{{\times }^{21}}{{C}_{1}}\] \[=24\times 23\times 22\times 21\] The total number of ways of selecting no pair \[=24\times 22\times 20\times 18\] \[\therefore \]Required probability \[=1-P\](no one getting a pair) \[=1-\frac{24\times 22\times 20\times 18}{24\times 23\times 22\times 21}=1-\frac{120}{161}\] \[=\frac{41}{161}\]
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