Home
Class 12
MATHS
In a n- sided regular polygon, the proba...

In a `n-` sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is `(2^n C_2)/(^(^(n C_(2-n)))C_2)` b. `(^(n(n-1))C_2)/(^(^(n C_(2-n)))C_2)` c. `(^n C_4)/(^(^(n C_(2-n)))C_2)` d. none of these

A

`(2^(n)C_(2))/(.^((.^(n)C_(2-n)))C_(2))`

B

`(.^(n(n-1))C_(2))/(.^((.^(n)C_(2)-n))C_(2))`

C

`(.^(n)C_(4))/(.^((.^(n)C_(2)-n))C_(2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
When 4 points are selected, we get one intersecting point. So, probability is
`(.^(n)C_(4))/(.^((.^(n)C_(2)-n))C_(2))`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Comprehension|14 Videos

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Match|2 Videos

  • PROBABILITY I

    CENGAGE ENGLISH|Exercise Exercise 9.3|7 Videos

  • PROBABILITY

    CENGAGE ENGLISH|Exercise Comprehension|2 Videos

  • PROBABILITY II

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

Similar Questions

Explore conceptually related problems

In a n- sided regular polygon, the probability that the two diagonal chosen at random will intersect inside the polygon is: (a.) (2^n C_2)/(^(^(n C_(2-n)))C_2) (b.) ("^(n(n-1))C_2)/(^(^(n C_(2-n)))C_2) (c.) (^n C_4)/(^(^(n C_2-n))C_2) (d.) none of these

(.^(n)C_(0))^(2)+(.^(n)C_(1))^(2)+(.^(n)C_(2))^(2)+ . . .+(.^(n)C_(n))^(2) equals

Prove that (^(2n)C_0)^2-(^(2n)C_1)^2+(^(2n)C_2)^2-+(^(2n)C_(2n))^2-(-1)^n^(2n)C_ndot

The middle term in the expansion of ((2x)/3-3/(2x^2))^(2n) is a. \ ^(2n)C_n b. (-1)^n\ ^(2n)C_(n\ )x^(-n) c. \ ^(2n)C_n x^(-n) d. none of these

If .^(n)C_(8) = .^(n)C_(2) , find .^(n)C_(2) .

Prove that "^n C_0^(2n)C_n-^n C_1^(2n-1)C_n+^n C_2xx^(2n-2)C_n++(-1)^n^n C_n^n C_n=1.

Evaluate .^(n)C_(0).^(n)C_(2)+2.^(n)C_(1).^(n)C_(3)+3.^(n)C_(2).^(n)C_(4)+"...."+(n-1).^(n)C_(n-2).^(n)C_(n) .

Prove that 1/(n+1)=(.^n C_1)/2-(2(.^n C_2))/3+(3(.^n C_3))/4- . . . +(-1^(n+1))(n*(.^n C_n))/(n+1) .

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

Prove that (""^(2n)C_(0))^2-(""^(2n)C_(1))^2+(""^(2n)C_(2))^2-.....+(-1)^n(""^(2n)C_(2n))^2=(-1)^n.""^(2n)C_(n)

CENGAGE ENGLISH-PROBABILITY I -MCQ
  1. Four die are thrown simultaneously. The probability that 4 and 3 appea...

    Text Solution

    |

  2. A 2n digit number starts with 2 and all its digits are prime, then the...

    Text Solution

    |

  3. In a n- sided regular polygon, the probability that the two diagonal c...

    Text Solution

    |

  4. A three-digit number is selected at random from the set of all thre...

    Text Solution

    |

  5. Two numbers a ,b are chosen from the set of integers 1, ,2 3, ..., 39....

    Text Solution

    |

  6. One mapping is selected at random from all mappings of the set S={1,2,...

    Text Solution

    |

  7. A composite number is selected at random from the first 30 natural ...

    Text Solution

    |

  8. Forty team play a tournament. Each team plays every other team just ...

    Text Solution

    |

  9. about to only mathematics

    Text Solution

    |

  10. A bag has 10 balls. Six ball are drawn in an attempt and replaced. The...

    Text Solution

    |

  11. Find the probability that a randomly chosen three-digit number has ...

    Text Solution

    |

  12. Let p,q be chosen one by one from the set {1, sqrt(2),sqrt(3), 2, e, p...

    Text Solution

    |

  13. Three integers are chosen at random from the set of first 20 natural ...

    Text Solution

    |

  14. 5 different balls are placed in 5 different boxes randomly. Find the p...

    Text Solution

    |

  15. There are 10 prizes, five As, there Bs and two Cs, placed in identi...

    Text Solution

    |

  16. A car is parked among N cars standing in a row, but not at either end....

    Text Solution

    |

  17. Let A be a set containing elements. A subset P of the set A is chosen ...

    Text Solution

    |

  18. about to only mathematics

    Text Solution

    |

  19. If a and b are chosen randomly from the set consisting of number 1, 2,...

    Text Solution

    |

  20. Mr. A lives at origin on the Cartesian plane and has his office at (4,...

    Text Solution

    |