AP EAMCET · Maths · Probability
In a shoe rack there are 4 pairs of shoes and 4 shoes are drawn one after the other at random without replacement. Then the probability of getting atleast one correct pair of shoes among the four shoes drawn is
- A \(\frac{8}{35}\)
- B \(\frac{27}{35}\)
- C \(\frac{1679}{1680}\)
- D \(\frac{1}{1680}\)
Answer & Solution
Correct Answer
(B) \(\frac{27}{35}\)
Step-by-step Solution
Detailed explanation
Total ways to draw 4 shoes from 8: \( \binom{8}{4} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} = 70 \) Ways to draw 4 shoes with no correct pairs (one shoe from each of 4 distinct pairs): \( \binom{4}{4} \times 2^4 = 1 \times 16 = 16 \) Probability of no…
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