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lookitswill

Permutations/Combinations: A coin is tossed 20 times and the heads and tails sequence is recorded. From among all the possible sequences of heads and tails, how many have exactly seven heads?

  • one year ago
  • one year ago

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  1. Tolio
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    it's just a combination: 20 choose 7 = 20C7\[\left(\begin{matrix}20 \\7 \end{matrix}\right)\] \[\frac{ 20! }{ (20-7)!7! }\] \[\frac{ 20! }{ 13! 7! }\] = 77,520

    • one year ago
  2. lookitswill
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    Oh, i understand it a bit better now. I put 40 instead of 20 because I thought it flipped 20 times and there are 2 heads..and multiply...it doesn't really make sense. Thanks for your hlep!

    • one year ago
  3. Azteck
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    Remember this equation. \[\left(\begin{matrix}n \\ r\end{matrix}\right)\] or \[_{n} C _{r}\] Formula: \[\frac{ n! }{ r!(n-r)! }\]

    • one year ago
  4. lookitswill
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    also, does "different" mean a permutation?

    • one year ago
  5. Azteck
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    different combinations?

    • one year ago
  6. lookitswill
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    like for example, How many DIFFERENT license plates consist of five symbols, either digits or letters? Would that be a permutation?

    • one year ago
  7. Azteck
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    differrent means number of combinations.

    • one year ago
  8. Azteck
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    Permutation is used to find the different combinations.

    • one year ago
  9. Tolio
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    in general try to think of permutations as being used when order matters and combinations when order doesn't the license plate example is a permutation because you have a choice of symbols for each ordered position: ex.: 3 letters then 3 numbers --> # of possibles = 26*26*26*10*10*10 the standard example for combinations is for choosing committee members i.e. a committee of Peter and Mary is no different than a one of Mary and Peter; a permutation would doubly count this. that why combinations have another factor in the denominator to divide by to correct for this. perm. = n!/(n-r)! and combin. = n!/((n-r)!*r!) if the license plate was a combination then ABC123 would be no different then B21CA3 or any other arrangement of the characters

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