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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

  1. A \(\frac{8}{35}\)
  2. B \(\frac{27}{35}\)
  3. C \(\frac{1679}{1680}\)
  4. D \(\frac{1}{1680}\)
Verified Solution

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…