Home
Class 11
MATHS
Prove that (n !)! is divisible by (n...

Prove that `(n !)!` is divisible by `(n !)^((n-1)!)`

Promotional Banner

Topper's Solved these Questions

  • LOGARITHM

    CENGAGE PUBLICATION|Exercise All Questions|177 Videos

  • PROBABILITY

    CENGAGE PUBLICATION|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Prove that (n !+1) is not divisible by any natural number between 2 and n

Prove that AA n,14^n-13n-1 is divisible by 13. (n in N)

Using the principle of mathematical induction prove that 3^(2n+1)+2^(n+2) is divisible by 7 [n in N]

Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,...

Using the principle of mathematical induction. Prove that (x^(n)-y^(n)) is divisible by (x-y) for all n in N .

By induction method prove that, (a^(n)+b^(n)) is divisible by (a+b) when n is an odd positive integer .

Prove that x^(n)-y^(n) is divisible by (x-y) for all n""inNN

Using principle of mathematical induction, prove that 7^(4^(n)) -1 is divisible by 2^(2n+3) for any natural number n.

If p be a natural number, then prove that, p^(n+1)+(p+1)^(2n-1) is divisible by (p^(2)+p+1) for every positive integer n.

Using the principle of mathematical induction, prove that (2^(3n)-1) is divisible by 7 for all n in N

CENGAGE PUBLICATION-PERMUTATIONS AND COMBINATIONS-All Questions
  1. Statement 1: The number of positive integral solutions of a b c=30 is ...

    Text Solution

    |

  2. Prove by combinatorial argument that .^(n+1)Cr=^n Cr+^n C(r-1)dot

    Text Solution

    |

  3. Prove that (n !)! is divisible by (n !)^((n-1)!)

    Text Solution

    |

  4. Column I, Column II Number of straight lines joining any two of ...

    Text Solution

    |

  5. If the number of selections of 6 different letters that can be made...

    Text Solution

    |

  6. If n1 and n2 are five-digit numbers, find the total number of ways...

    Text Solution

    |

  7. If n1a n dn2 are five-digit numbers, find the total number of ways ...

    Text Solution

    |

  8. If a denotes the number of permutations of (x+2) things taken all at a...

    Text Solution

    |

  9. If .^nPr = .^nP(r + 1) and .^nCr = .^nC(r-1) then the value of n + r...

    Text Solution

    |

  10. Let n be the number of ways in which 5 boys and 5 girls can stand in a...

    Text Solution

    |

  11. In how many ways can a pack of 52 cards divided in 4 sets, three of th...

    Text Solution

    |

  12. Let f(n)=sum(r=0)^nsum(k=r)^n(kC r) Find the total number of divisor...

    Text Solution

    |

  13. True or false: The product of any r consecutive natural numbers is al...

    Text Solution

    |

  14. Statement 1: Number of zeros at the end of 50! is equal to 12. State...

    Text Solution

    |

  15. Using permutation or otherwise, prove that (n^2)!/(n!)^n is an integer...

    Text Solution

    |

  16. A number of 18 guests have to be seated, half on each side of a lon...

    Text Solution

    |

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

    Text Solution

    |

  18. A box contains 2 white balls, 3 black balls & 4 red balls. In how many...

    Text Solution

    |

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

    Text Solution

    |

  20. A forecast is to be made of the results of five cricket matches, eac...

    Text Solution

    |