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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2017 · Mathematics · Permutation and Combination

Five sticks of length 1,3,5,7 and 9 feet are given. Three of these...

Five sticks of length 1,3,5,7 and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can from a triangle?

Options

  1. A0.50.5
  2. B0.40.4
  3. C0.30.3
  4. D00

Correct answer

C. 0.30.3

Step-by-step solution

3 sticks can be selected from 5 sticks in 5c3{ }^5 \mathrm{c}_3 ways 5c3=10{ }^5 \mathrm{c}_3=10 Probability that selected sticks from a triangle is P(E)\mathrm{P}(\mathrm{E})n(E)=4c3−1=4×3×2×13×2×1−1=4−1=3.∴p(E)=310=0.3\begin{aligned} & n(E)={ }^4 c_3-1=\frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1}-1=4-1=3. \\ & \therefore p(E)=\frac{3}{10}=0.3\end{aligned}$$
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