Results 1 to 3 of 3

Math Help - simple factorial question

  1. #1
    Newbie
    Joined
    May 2008
    Posts
    2

    simple factorial question

    Hi All

    I have 20 different coloured bangles.
    Customers buy 60, in any combination.
    (e.g. 60 of same colour, 5 each of all 20 colours, etc)
    How many different combinations are possible?
    (I realise it's somewhere between 20 factorial and 60 factorial, but then I'm stuck.)
    Expressing the answer in the form n.nn x 10 to power y would be very helpful.

    Thanks
    James
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by james maths questioner View Post
    Hi All

    I have 20 different coloured bangles.
    Customers buy 60, in any combination.
    (e.g. 60 of same colour, 5 each of all 20 colours, etc) Mr F says: 5 each of all 20 colours is 100, not 60 .....?
    How many different combinations are possible?
    (I realise it's somewhere between 20 factorial and 60 factorial, but then I'm stuck.) Mr F asks: why do you think this?
    Expressing the answer in the form n.nn x 10 to power y would be very helpful.

    Thanks
    James
    This is a combinations with replacement problem:

    With repetition allowed, the number of different combinations of r objects chosen from n distinguishable objects is

    {n + r - 1 \choose r}.

    So for your problem I get approximately 8.83829 \times 10^{18} (a number which is less than 20! by the way).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2008
    Posts
    2

    simple factorial problem

    Hi Mr F

    1. Yes you're right - it's 3 of each colour - sorry.
    2. I had assumed that the answer would be more than 20 factorial, because it would be 20 factorial if they ordered 20, and thay can order 60 (although the number of colours remain cosntant at 20). I'm afraid I'm a beta-brain!
    3. Thank you for your answer - which is clearly billions, even in the old-fashioned UK definition of 10 to the 12th.

    James
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Factorial question
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: January 18th 2011, 04:08 PM
  2. factorial question
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 31st 2010, 10:28 AM
  3. 3x2 Factorial Design Question
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: January 4th 2010, 09:53 AM
  4. [SOLVED] Factorial series question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 30th 2009, 05:49 PM
  5. Replies: 6
    Last Post: September 12th 2007, 07:48 AM

Search Tags


/mathhelpforum @mathhelpforum