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Life Group Title

How is choosing a boy and a girl from 12 boys and 12 girls to represent a club different from choosing two girls from 12 girls to be president and treasurer of the club?

  • one year ago
  • one year ago

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  1. Shadowys Group Title
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    the first involves 24 choices. the other involve 12 choices.

    • one year ago
  2. Life Group Title
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    thats what i thought, thanks for the clarity

    • one year ago
  3. Shadowys Group Title
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    lol you're welcome :)

    • one year ago
  4. kropot72 Group Title
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    When considering choosing a boy and a girl from 12 boys and 12 girls there are 12 choices of girl for each boy selected. So the total number of ways of choosing is:\[12\times 12\] When choosing 2 girls from 12 to be president and treasurer of the club there are 2 ways of assigning the offices for each pair chosen. So in this case the number of ways of choosing is: \[12P2=\frac{12!}{(12-2)!}=12\times 11\]

    • one year ago
  5. Life Group Title
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    What does the exclamation point mean?

    • one year ago
  6. kropot72 Group Title
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    The exclamation point indicates a factorial. A factorial is the product of all the positive integers from 1 up to and including a given integer. The symbol is n! where n is the given integer. So 5 factorial is written 5! and means \[5\times 4\times 3\times 2\times 1(=120)\]

    • one year ago
  7. kropot72 Group Title
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    Also 12P2 means the number of permutations of 12 different things taken 2 at a time.

    • one year ago
  8. Life Group Title
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    Thanks :)

    • one year ago
  9. kropot72 Group Title
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    You're welcome :) You can look at the choice of president and treasurer from the 12 girls very simply as follows: If one of the 12 girls is chosen as president there are 11 choices for treasurer. So for each one of the girls chosen as president there are 11 choices for treasurer. Going through each in sequence it will be seen that each one if the girls has a possibility of being either president or treasurer and the total number of ways of choosing is \[12\times 11\]

    • one year ago
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