Home
Class 12
MATHS
The numbers 1, 2, 3, ..., n are arrange ...

The numbers 1, 2, 3, ..., `n` are arrange in a random order. The probability that the digits 1, 2, 3, .., `k( k < n)` appear as neighbours in that order is

A

`((n-k)!)/(n!)`

B

`((n-k+1)!)/(.^nC_k)`

C

`(n-k)/(,^nC_k)`

D

`(k!)/(n!)`

Text Solution

Verified by Experts

The correct Answer is:
(b)
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Probability Exercise 1: Single Option Single Correct Type Question|1 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • PROBABILITY

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 4|15 Videos

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|28 Videos

  • PRODUCT OF VECTORS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|51 Videos

Similar Questions

Explore conceptually related problems

Five different digits from the set of numbers {1, 2, 3, 4, 5, 6, 7} are written in random order. Find the probability that five-digit number thus formed is divisible by 9.

Seven digits from the numbers 1 to 9 are written in random order. If the probability that this seven digit number divisible by 9 is p, then the value of 18p is

A bag contains 30 tickets numbered from 1 to 30 . Five tickets are drawn at random and arranged in ascending order . Find the probability that the third number is 20. (ii) a bag contains 50 tickets numbered 1,2,3 ……, 50 of which five are drawn at random and arranged in ascending order of magnitude (x_(1)ltx_(2)ltx_(3)ltx_(4)ltx_(5)) . What is the probability that x_(3)=30 .?

The digits 1,2,3,4,5,6,7,8 and 9 are written in random order to form a nine digit number. The probability that this number is divisible by 4, is

If a digit is chosen at random from the digits 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9 , then the probability that the digit is even, is (a) 4/9 (b) 5/9 (c) 1/9 (d) 2/3

If a digit is chosen at random from the digits 1,\ 2,\ 3,\ 4,\ 5,\ 6,\ 7,\ 8,\ 9 then, the probability that the digit is a multiple of 3 is (a) 1/3 (b) 2/3 (c) 1/9 (d) 2/9

If four whole numbers taken at random are multiplied together, then find the probability that the last digit in the product is 1,3,7 or 9.

A five-digit number is written down at random. The probability that the number is divisible by 5 and no two consecutive digits are Identical is a. 1/5 b. 1/5(9/(10))^3 c. (3/5)^4 d. none of these

Three-digit numbers are formed using the digits 0,1, 2, 3, 4, 5 without repetition of digits. If a number is chosen at random, then the probability that the digits either increase or decrease, is

Two numbers a and b are chosen at random from the set {1,2,3,..,3n}. The probability that a^(3)+b^(3) is divisible by 3, is

ARIHANT MATHS ENGLISH-PROBABILITY-Exercise (Single Option Correct Type Questions)
  1. Three different numbers are selected at random from the set A = (1, 2...

    Text Solution

    |

  2. The numbers 1,2,3,.., n are arranged in a random order. The probabilit...

    Text Solution

    |

  3. The numbers 1, 2, 3, ..., n are arrange in a random order. The probabi...

    Text Solution

    |

  4. Four identical dice are rolled once. The probability that at least thr...

    Text Solution

    |

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

    Text Solution

    |

  6. If two of the 64 squares are chosen at random on a chess board, the pr...

    Text Solution

    |

  7. A letter is known to have come from CHENNAI, JAIPUR, NAINITAL, DUBAI a...

    Text Solution

    |

  8. Let a die is loaded in such a way that prime number faces are twice as...

    Text Solution

    |

  9. One ticket is selected at random from 100 tickets numbered 00,01,02, …...

    Text Solution

    |

  10. All the spades are taken out from a pack of cards. From these cards; c...

    Text Solution

    |

  11. A number is selected at random from the first 25 natural numbers. I...

    Text Solution

    |

  12. A bag contains 50 tickets numbered 1, 2, 3, .., 50 of which five are ...

    Text Solution

    |

  13. India play two matches each with West Indies and Australia. In any ...

    Text Solution

    |

  14. Three six faced dice are tossed together, then the probability that ex...

    Text Solution

    |

  15. Three six-faced dice are thrown together. The probability that the sum...

    Text Solution

    |

  16. A book contains 1000 pages. A page is chosen at random. Find the proba...

    Text Solution

    |

  17. A bag contains 4 tickets numbered 00, 01, 10 and 11. Four tickets are ...

    Text Solution

    |

  18. Fifteen coupens are numbered 1,2,3,...15 respectively. Seven coupons a...

    Text Solution

    |

  19. The box contains tickets numbered from 1 to 20. Three tickets are draw...

    Text Solution

    |

  20. An unbiased die with faces marked 1,2,3,45 and 6 is rolled four times...

    Text Solution

    |