MHT CET · Maths · Permutation Combination
Three numbers are selected randomly between 1 to 20 . Then, the probability that they are consecutive numbers will be
- A \(\frac{7}{190}\)
- B \(\frac{3}{190}\)
- C \(\frac{5}{190}\)
- D \(\frac{1}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{190}\)
Step-by-step Solution
Detailed explanation
Number of sample space for selecting three numbers between 1 to \(20={ }^{20} C_{3}\)
Number of ways that they are consecutive numbers \(=18\).
\(\therefore\) Required probability
\(=\frac{18}{20} C_{3}=\frac{18 \times 3 \times 2}{20 \times 19 \times 18}\)
\(=\frac{3}{190}\)
Number of ways that they are consecutive numbers \(=18\).
\(\therefore\) Required probability
\(=\frac{18}{20} C_{3}=\frac{18 \times 3 \times 2}{20 \times 19 \times 18}\)
\(=\frac{3}{190}\)
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