Results 1 to 2 of 2

Math Help - Permutation and Combination Help!

  1. #1
    Member looi76's Avatar
    Joined
    Jan 2008
    Posts
    185

    Permutation and Combination Help!

    Question:
    A coin is tossed 10 times.
    (a) How many different sequences of heads and tails are possible?
    (b) How many different sequences containing six heads and four tails are possible?
    (c) What is the probability of getting si heads and four tails?


    Attempt:
    (a) = 0 Heads or 1 Heads or 2 Heads or 3 Heads or 4 Heads or 5 Heads or 6 Heads or 7 Heads or 8 Heads or 9 Heads or 10 Heads.
    = 10C0 + 10C1 + 10C2 + 10C3 + 10C4 + 10C5 + 10C6 + 10C7 + 10C8 + 10C9  + 10C10
    = 1024

    (b) = 10C6+10C4 = 420

    (c) No Idea!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,678
    Thanks
    611
    Hello, looi76!

    A coin is tossed 10 times.
    (a) How many different sequences of heads and tails are possible?
    Your answer is correct, but there's an easier approach.

    For each coin there are two possible states: Heads or Tails.

    . . With ten coins, there are: . 2^{10} \:=\:1024 possible outcomes.



    (b) How many different sequences containing 6 Heads and 4 Tails are possible?
    There are: . {10\choose6,4} \:=\:210 ways.



    (c) What is the probability of getting 6 Heads and 4 Tails?
    There are 210 ways to get 6 Heads and 4 Tails
    . . out of the 1024 possible outcomes.

    Therefore: . P(\text{6 Heads, 4 Tails}) \;=\;\frac{210}{1024} \;=\;\frac{105}{512}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. combination/permutation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: October 16th 2008, 11:40 PM
  2. permutation and combination
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 11th 2008, 07:42 AM
  3. Permutation and Combination
    Posted in the Statistics Forum
    Replies: 2
    Last Post: September 28th 2008, 09:37 PM
  4. Permutation and Combination
    Posted in the Statistics Forum
    Replies: 5
    Last Post: February 16th 2008, 01:17 PM
  5. Combination/Permutation
    Posted in the Statistics Forum
    Replies: 6
    Last Post: September 11th 2007, 03:42 PM

Search Tags


/mathhelpforum @mathhelpforum