Home
Class 12
MATHS
Three of the six vertices of a regular h...

Three of the six vertices of a regular hexagon are chosen the random. What is the probability that the triangle with these vertices is equilateral.

A

`(1)/(2)`

B

`(1)/(5)`

C

`(1)/(10)`

D

`(1)/(20)`

Text Solution

Verified by Experts

Total number of triangles which can be formed is equal to `.^(6)C_(3)=(6xx5xx4)/(1xx3xx3)=20`
Number of equilateral triangle = 2
`:.` Required probability `=(2)/(20)=(1)/(10)`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise Physics, SECTION-1 (PART-A)|5 Videos

  • TEST PAPERS

    BANSAL|Exercise Physics, SECTION-1 (PART-A) [COMPREHENSION TYPE]|2 Videos

  • TEST PAPERS

    BANSAL|Exercise Math|15 Videos

  • PROBABILITY

    BANSAL|Exercise All Questions|1 Videos

  • THERMODYNAMICS

    BANSAL|Exercise Match the column|7 Videos

Similar Questions

Explore conceptually related problems

Three of six vertices of a regular hexagon are chosen at random.The probability that the triangle with three vertices is equilateral is (a) (1)/(2) (b) (1)/(5) (c) (1)/(10) (d) (1)/(20)

Three vertices are chosen at random from the vertices of a regular hexagon then The probability that the triangle with these vertices is an equilateral triangle is equal to

If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is :

If four vertices a regular octagon are chosen at random, then the probability that the quadrilateral formed by them is a rectangle is

Two vertices of an equilateral triangle are origin and (4, 0). What is the area of the triangle ?

BANSAL-TEST PAPERS-MATHS
  1. If the area of the triangle formed by the points z, z +iz and iz on th...

    Text Solution

    |

  2. In the parabola y^2=4a x , then tangent at P whose abscissa is equal t...

    Text Solution

    |

  3. Three of the six vertices of a regular hexagon are chosen the rando...

    Text Solution

    |

  4. Out of 3n consecutive natural numbers, 3 natural numbers are chosen at...

    Text Solution

    |

  5. If w=alpha+ibeta where Beta 0 and z ne 1 satisfies the condition that...

    Text Solution

    |

  6. The equation of the normal to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(...

    Text Solution

    |

  7. If z1 and z2 are two non zero complex number such that|z1+z2|=|z1|+|z2...

    Text Solution

    |

  8. Find the equation of the hyperbola which has 3x-4y+7=0 and 4x+3y+1=0 a...

    Text Solution

    |

  9. India and Pakistan play a series of 'n' one day matches and probabilit...

    Text Solution

    |

  10. India and Pakistan play a series of 'n' one day matches and probabilit...

    Text Solution

    |

  11. Let a hyperbola passes through the focus of the ellipse 16x^(2)+25y^(2...

    Text Solution

    |

  12. Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)-(...

    Text Solution

    |

  13. Consider the chords of the parabola y^(2)=4x which touches the hyperbo...

    Text Solution

    |

  14. Consider the chords of the parabola y^(2)=4x which touches the hyperbo...

    Text Solution

    |

  15. A number is chosen at random from the set {1,2,3,4,....,n} . Let E(1) ...

    Text Solution

    |

  16. A (-1, 0) and B (2, 0) are two given points. A point M is moving in s...

    Text Solution

    |

  17. If |Z-4/Z|=2 then maximum value of |Z| is equal to

    Text Solution

    |

  18. Which of the following statement(s) is (are) correct ?

    Text Solution

    |

  19. |(Z1 - 1)/(Z1 - 4)| = 2 & | (Z2 - 4)/ (Z2 - 1)| = 2 the |Z1 - Z2|max ...

    Text Solution

    |

  20. The equation of a parabola having its focus at S(2,0) and one extremit...

    Text Solution

    |