Home
Class 12
MATHS
Let A be a set of n (>=3) distinct eleme...

Let A be a set of n `(>=3)` distinct elements. The number of triplets `(x, y, z)` of the A elements in which at least two coordinates is equal to

A

`.^(n)P_(3)`

B

`n^(3)-.^(n)P_(3)`

C

`3n^(2)-2n`

D

`3n^(2)(n-1)`

Text Solution

Verified by Experts

The correct Answer is:
B
Required number of triplets=Total number of triplets without restrictions-number of triplets with all different coordinates
`=n^()-.^(n)P_(3)`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|10 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|15 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise For Session 7|5 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|36 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

Let A be a set of n(>=3) distance elements. The number of triplets (x,y,z) of the A elements in which at least two coordinates is equal to a.^(n)P_(3) b.n^(3)-^(n)P_(3) c.3n^(2)-2n d.3n^(2)-(n-1)

Let A be a finie set containing n distinct elements. The number of relations that can be defined on A is

Let A be a finite set containing n distinct elements. The number of functions that can be defined from A to A is

A is a set having 6 distinct elements. The number of distinct functions from A to A which are not bijection is

A set contains 5 elements. The number of subsets of the set which contain atmost n element is

Let A be a set containing 10 distinct elements, then the total number of distinct functions from A to A is

ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Single Option Correct Type Questions)
  1. On a railway there are 20 stations. The number of different tickets re...

    Text Solution

    |

  2. A is a set containing n elements. A subset P of A is chosen at random....

    Text Solution

    |

  3. The straight lines I(1),I(2),I(3) are paralled and lie in the same pla...

    Text Solution

    |

  4. Let A be a set of n (>=3) distinct elements. The number of triplets (x...

    Text Solution

    |

  5. The total number of five-digit numbers of different digits in which...

    Text Solution

    |

  6. The total number of words that can be formed using all letters of the ...

    Text Solution

    |

  7. A man has three friends. The number of ways he can invite one frien...

    Text Solution

    |

  8. The number of three digit numbers of the form xyz such that x lt y , z...

    Text Solution

    |

  9. The letters of the word 'MEERUT' are arranged in all possible ways as ...

    Text Solution

    |

  10. The number of ways in which 10 condidates A(1),A(2),......,A(10) can b...

    Text Solution

    |

  11. Let A be the set of 4-digit numbers a1 a2 a3 a4 where a1 > a2 > a3 > a...

    Text Solution

    |

  12. Find the number of distinct rational numbers x such that o<x<1a n dx=p...

    Text Solution

    |

  13. The total number of positive integral solutions for (x, y, z) such tha...

    Text Solution

    |

  14. ABCD is a convex quadrilateral and 3, 4, 5, and 6 points are marked...

    Text Solution

    |

  15. In how many ways can a team of 6 horses be selected out of a stud o...

    Text Solution

    |

  16. The number of polynomials of the form x^(3)+ax^(2)+bx+c that are divis...

    Text Solution

    |

  17. Let x(1),x(2),x(3), . . .,x(k) be the divisors of positive integer 'n'...

    Text Solution

    |

  18. The total number of function f from the set (1,2,3) into the set (1,2,...

    Text Solution

    |

  19. Ten persons numbered 1, ,2 ..,10 play a chess tournament, each play...

    Text Solution

    |

  20. In the next world cup of cricket there will be 12 teams, divided equal...

    Text Solution

    |