Results 1 to 8 of 8

Math Help - how to find the number of arrangements possible for a particular draw from crads

  1. #1
    Newbie
    Joined
    Jul 2010
    Posts
    6

    Question how to find the number of arrangements possible for a particular draw from crads

    There are 25 cards with 5 signs and each sign contains digits 1 to 5 in them. What is the maximum number of arrangements possible in 5 cards drawn from them? numbers can be repeated but signs cannot be repeated and in each draw of 5 cards there should be all the five signs in it without repetition and without the absence of any sign. What is the general formula for this? Say n signs X n numbers = n^2 cards
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1

    More information please

    Hello dijinj

    I'm sorry, I just don't understand what the question means?
    Quote Originally Posted by dijinj View Post
    There are 25 cards with 5 signs and each sign contains digits 1 to 5 in them...
    So a 'sign' contains digits 1 to 5. How many digits make up a sign? All of them? Just one? What?
    ...numbers can be repeated but signs cannot be repeated...
    What is meant by a 'number'? A set of digits? A single digit? What?

    Unless you can define much more accurately what you mean, it's not going to be possible to give you any help.

    Do you have a statement of the original question? If so, let's see it in full, and we'll take it from there.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2010
    Posts
    6
    just like normal playing cards has 52 cards with four signs( hearts, ispade, etc) and each sign( for exapmple ispade) has a number among 1-10 then j k q. this system has 25 cards and five signs each sign has a number among 1-5 on them. total no: of cards bearing same sign is five just like in playing cards, where it is 13.

    In a draw the numbers can be repeated for example in one draw all the five card can be of number 5 or four cards can be 5 and fifth one can be say 2. but in a draw the sign can not be repeated it must be unique for each cards that has been drawn. for example first card can be claver second card can be dice,, third can be hearts forth can be ispade and fifth can be with a circle sign on it, order of signs is not important but it must be unique in each card in every draw.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Can permutations with repetition formula can directly be applied to here (n^r), problem is uniqueness of signs. only number on cards can be repeated
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello dijinj

    OK. So let me see if I understand the question. A pack of 25 cards contains five 'suits' (signs), each 'suit' containing five different cards. We simply have to find the number of possible arrangements of five cards, where each card is chosen from a different 'suit'.

    The answer is this:
    There are \displaystyle 5! ways of arranging the different 'suits'. There are \displaystyle 5 ways of choosing each card from within its suit. So the total number of arrangements is \displaystyle 5^5\times5!.
    If you didn't really mean the number of different arrangements, but instead you meant the number of different selections, then the answer is just \displaystyle 5^5.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    769
    Hello, dijinj!

    I must make some assumptions . . .


    There are 25 cards with 5 suits and each suit contains digits 1 to 5.

    What is the maximum number of arrangements of 5 cards drawn from them?
    All five suits must be in the arrangement.

    It says "arrangements"; I assume that the order of the cards is important.


    We have these 25 cards:

    . . \begin{array}{ccccc}A\spadesuit & 2\spadesuit & 3\spadesuit & 4\spadesuit & 5\spadesuit \\<br />
A\heartsuit & 2\heartsuit & 3\heartsuit & 4\heartsuit & 5\heartsuit \\<br />
A\clubsuit & 2\clubsuit & 3\clubsuit & 4\clubsuit & 5\clubsuit \\<br />
A\diamondsuit & 2\diamondsuit & 3\diamondsuit & 4\diamondsuit & 5\diamondsuit \\<br />
A\bigstar & 2\bigstar & 3\bigstar & 4\bigstar & 5\bigstar<br />
\end{array}


    The first card can be any of the 25 cards.

    The second card can be any of the 20 cards of a second suit.

    The third card can be any of the 15 cards of a third suit.

    The fourth card can be any of the 10 cards of a fourth suit.

    The fifth card must be one the remaining 5 cards of the fifth suit.


    There are: . 25\cdot20\cdot15\cdot10\cdot5 \:=\:375,000 possible arrangements.


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    If the order of the cards is not important, divide by 5!

    . . \text{There are: }\;\dfrac{375,000}{120} \;=\;3125\:\:selections \text{ of 5 cards.}



    These answers are identical to Grandad's.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Jul 2010
    Posts
    6
    Thanks, Thank you for your kind help and answers!
    Once again thanks!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Member Chokfull's Avatar
    Joined
    May 2009
    From
    Neverland
    Posts
    108
    Thanks
    1
    Quote Originally Posted by dijinj View Post
    There are 25 cards with 5 signs and each sign contains digits 1 to 5 in them. What is the maximum number of arrangements possible in 5 cards drawn from them? numbers can be repeated but signs cannot be repeated and in each draw of 5 cards there should be all the five signs in it without repetition and without the absence of any sign. What is the general formula for this? Say n signs X n numbers = n^2 cards
    The problem has already been solved but I would like to note that another way to state this also makes it much simpler:

    How many arrangements are there of the numbers 1-5? The numbers can be repeated.

    Since the signs cannot be repeated they are irrelevant.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: June 19th 2011, 04:41 PM
  2. Find Number of Arrangements
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: October 6th 2010, 04:57 PM
  3. Number of arrangements
    Posted in the Discrete Math Forum
    Replies: 13
    Last Post: October 3rd 2010, 11:38 AM
  4. Number of arrangements
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 9th 2009, 08:33 AM
  5. Number of arrangements
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 25th 2009, 06:35 PM

Search Tags


/mathhelpforum @mathhelpforum