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AP EAMCET · Maths · Permutation Combination

A company representative is distributing 5 identical samples of a product among 12 houses in a row such that each house gets at most one sample. The probability that no two consecutive houses get one sample is

  1. A \(\frac{7}{99}\)
  2. B \(\frac{5}{12}\)
  3. C \(\frac{4}{13}\)
  4. D \(\frac{5}{31}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{7}{99}\)

Step-by-step Solution

Detailed explanation

Total ways: \( \binom{12}{5} = \frac{12 \times 11 \times 10 \times 9 \times 8}{5 \times 4 \times 3 \times 2 \times 1} = 792 \) Favorable ways (no two consecutive): \( \binom{12-5+1}{5} = \binom{8}{5} = \frac{8 \times 7 \times 6}{3 \times 2 \times 1} = 56 \) Probability:…