AP EAMCET · Maths · Probability
Three numbers are chosen from 1 to 30. The probability that they are not three consecutive numbers is
- A \(\frac{1}{145}\)
- B \(\frac{142}{145}\)
- C \(\frac{143}{145}\)
- D \(\frac{144}{145}\)
Answer & Solution
Correct Answer
(D) \(\frac{144}{145}\)
Step-by-step Solution
Detailed explanation
\( \text{Total combinations} = \binom{30}{3} = \frac{30 \times 29 \times 28}{3 \times 2 \times 1} = 4060 \) \( \text{Consecutive triplets} = (1,2,3), \dots, (28,29,30) = 28 \) \( P(\text{consecutive}) = \frac{28}{4060} = \frac{1}{145} \)…
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