Question

A box contains 6 wooden, straight sticks of the following lengths (in inches): 2, 3, 5, 7, 11, and 13. Three sticks are drawn at random from the box without looking. What is the probability that a triangle can be formed with the sticks that are drawn?

Answer 1

`(1)/(4)`

Explanation:

given,

straight stick of length = 2, 3, 5, 7, 11, and 13.

For a triangle to form third side of the sum of the two side of the triangle should be greater than third.

so the possibility of triangle formed

5,11,13

7,11,13

3,11,13

7,5,11

5,3,7

ways of drawing 3 wooden sticks

⁶C₃ =
`(6!)/(3!* 3!)`= 20

so the probability =
`(5)/(20)`

=
`(1)/(4)`