Results 1 to 3 of 3

Math Help - binomial problem!

  1. #1
    Member
    Joined
    Jul 2011
    Posts
    93

    binomial problem!

    5 digits numbers is formed by using the digits 0,1,2,3,4 and 5 without repetition. find the probability that the number is divisible by 6?

    pls help out here, confuse!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,802
    Thanks
    687

    Re: binomial problem!

    Hello, lawochekel!

    I'll explain it using baby-steps.


    Five-digit numbers are formed by using the digits {0,1,2,3,4,5} without repetition.
    Find the probability that the number is divisible by 6.

    There are 6!= 720 possible five-digit numbers.

    To be divisible by 6, the number must be:
    . . (1) divisible by 3 ... the sum of its digits must be divisible by 3.
    . . (2) even ... the last digit must be even.


    There are two sets of digits whose sums are divisible by 3:
    . . \{0,1,2,4,5\}\:\text{ and }\,\{1,2,3,4,5\}

    Consider \{0,1,2,4,5\}
    The last digit must be even: \{0,2,4\}, 3 choices.
    The other four digits can be arranged in 4! ways.
    Hence, there are:. 3\cdot4! \,=\,72 numbers divisible by 6.

    Consider \{1,2,3,4,5\}
    The last digit must be even: \{2,4\}, 2 choices.
    The other four digits can be arranged in 4! ways.
    Hence, there are:. 2\cdot4! \,=\,48 more numbers divisible by 6.

    Hence, there are:. 72 + 48 \,=\,120 numbers which are divisible by 6.


    Therefore:. P(\text{div by 6}) \:=\:\frac{120}{720} \:=\:\frac{1}{6}

    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,789
    Thanks
    1683
    Awards
    1

    Re: binomial problem!

    Quote Originally Posted by Soroban View Post
    There are 6!= 720 possible five-digit numbers.
    Are you counting 05421 as a five-digit number?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Binomial Problem!!
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: May 31st 2010, 07:14 PM
  2. Binomial Coefficient Problem.
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: March 30th 2009, 12:35 PM
  3. problem on binomial
    Posted in the Algebra Forum
    Replies: 7
    Last Post: June 18th 2008, 03:01 AM
  4. another binomial problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 11th 2008, 01:44 AM
  5. a binomial thm problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: January 10th 2008, 09:28 PM

Search Tags


/mathhelpforum @mathhelpforum