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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Probability

NDA 2024 · Mathematics · Probability

Three distinct natural numbers are chosen at random from 1 to 10....

Three distinct natural numbers are chosen at random from 1 to 10. What is the probability that they are consecutive?

Options

  1. A112\frac{1}{12}
  2. B340\frac{3}{40}
  3. C115\frac{1}{15}
  4. D7120\frac{7}{120}

Correct answer

C. 115\frac{1}{15}

Step-by-step solution

Three distinct natural numbers are chosen from 1 to 10. n(s)=10c3\mathrm{n}(\mathrm{s})=10 \mathrm{c}_3 Favourable outcomes =(1,2,3),(2,3,4),(3,4,5),(4,5=(1,2,3),(2,3,4),(3,4,5),(4,5, 6),(5,6,7),(6,7,8),(7,8,9),(8,9,10)n(E)=8∴P(E)=n(E)n(S)=8103=8×7!×3!10!=8×3×2×110×9×8=1156),(5,6,7),(6,7,8),(7,8,9),(8,9,10)\mathrm{n}(\mathrm{E})=8\therefore \quad P(E)=\frac{n(E)}{n(S)}=\frac{8}{10_3}=\frac{8 \times 7!\times 3!}{10!}=\frac{8 \times 3 \times 2 \times 1}{10 \times 9 \times 8}=\frac{1}{15}
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