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Permutation and combination problem with coins

  1. Mar 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Hello, it is a permutation / combination approach question, however, having thought about an hour i can't get any idea how it should be solved.

    Question is

    A coin is flipped n times, where n>=3

    Find the number of ways to obtain

    (i) exactly two heads
    (ii) at least 2 heads

    I am not asking for answers. I have the answers but I don't understand... I don't know how to understand the problem from the definition of permutation and combination.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Mar 2, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    To get exactly two heads, you must also get n- 2 tails. How many ways can you arrange HHTTTT...T?

    "At least two heads" would mean "NOT 0 heads or 1 head". There are [itex]2^n[/itex] ways to arrange n letters that can be "H" or "T". How many ways are there to arrange HTTTT...T?
     
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