Recent content by kingtaf

  1. K

    How to calculate actuarial present value

    I am not sure if this was the right forum. if not let me know. An auto repair shop plans to sell a new brand of car battery with a 4-year warranty. Given: (i) If the battery fails within 4 years, the shop will refund a pro-rata share of the purchase price at the moment of failure. (ii)...
  2. K

    Faces of the cube are colored

    Check it out: 'Each of the faces of the cube are colored by a diff erent of six fi xed colors. How many of the colorings are distinct?' I figured it would be 6!,very simple. But no,there's a trick, can u figure it out!!!!
  3. K

    License Plate

    A witness to a hit-and-run accident tells the police that the license plate of the car in the accident, which contains three letters followed by three digits, starts with the latters AS and contains both the digits 1 and 2. How many different license plates fit the description?
  4. K

    Perfect number

    Show that if (2^p) -1 is prime then (2^(p-1)) * ((2^p) - 1) is perfect
  5. K

    Finite subsets of N

    Prove that the collection F(N) of all fi nite subsets of N (natural numbers) is countable.
  6. K

    Prime factorial proof

    Thank you everyone I got it. After Hoch's hint using n! - 1, I figured it out. It's actually pretty simple. I feel really stupid!
  7. K

    Prime factorial proof

    I considered Bertrand's Postulate but as hochs said it got messy.i still cant figure it out
  8. K

    Prime factorial proof

    Prove or disprove: If n is an integer and n > 2, then there exists a prime p such that n < p < n!.