TS EAMCET · Maths · Probability
Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is
- A \(\frac{9}{20}\)
- B \(\frac{1}{5}\)
- C \(\frac{11}{30}\)
- D \(\frac{17}{60}\)
Answer & Solution
Correct Answer
(C) \(\frac{11}{30}\)
Step-by-step Solution
Detailed explanation
Number of way to matched 5 men with wives \(=5 \cdot 4 \cdot 3 \cdot 2 \cdot 1=120\) Number of way no man is matched with none of his wife \(=D_5=5!\left(1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!}+\frac{1}{4!}-\frac{1}{5!}\right)=44\) \(\therefore\) Probability…
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