A set of integers is given as (3,6,8,14,17). What is the probability that a tr

Question -

A set of integers is given as (3,6,8,14,17). What is the probability that a triangle can be constructed.?

Options:

A .

\frac{3}{5}

B .

\frac{3}{10}

C .

\frac{1}{10}

D .

\frac{5}{10}

Answer: Option B
:
B

Any 3 points can be selected in $^{5} C_{3}$ i.e 10 ways.

For forming a triangle sum of two sides should be greater than the $3^{r d}$ side.

Hence following set of integers can be selected

(3,6,8)

(6,8,17)

(8,14,17)

Hence P(Triangle is formed)= $\frac{3}{10}$

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