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Math Help - Probabilty: Some Answers That Need Checking and Etc.

  1. #1
    Newbie stmsnyder1's Avatar
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    Probabilty: Some Answers That Need Checking and Etc.

    Hi,


    If anyone can please check what I have done, that would be awesome,

    62. Class rings: You want to purchase a class ring. The ring can be made from three different metals, six different designs, and twelve stones. How many different class rings are possible? 216 class rings are possible.

    I used the fundamental counting principal. 12*3*6=216 different rings.

    64. Photography: A photographer lines up 15 members of a family in a single line in order to take a single photograph. How many different ways can the photographer arrange the family for the picture?

    The photographer can arrange the family in 225 different ways because he wants them in a single line for a single photograph. There are 15 family members, and 15^2= 225 different ways.

    66. Music: The window of a music store has eight stands in a fixed position where instruments can be displayed. In how many ways can three identical guitars, two identical keyboards, and three identical violins be displayed?

    I used the fundamental counting principal, and got 18. 3*2*3=18 But I know that's not right because the instruments are identical, it's not like they're different. Is the answer 3?


    Thank you very much
    Isabel
    Last edited by stmsnyder1; February 7th 2009 at 01:08 PM. Reason: Distributing questions over several threads
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  2. #2
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    Quote Originally Posted by stmsnyder1 View Post
    Hi,


    If anyone can please check what I have done, that would be awesome,

    62. Class rings: You want to purchase a class ring. The ring can be made from three different metals, six different designs, and twelve stones. How many different class rings are possible? 216 class rings are possible.

    I used the fundamental counting principal. 12*3*6=216 different rings. Mr F says: Correct.


    64. Photography: A photographer lines up 15 members of a family in a single line in order to take a single photograph. How many different ways can the photographer arrange the family for the picture?

    The photographer can arrange the family in 225 different ways because he wants them in a single line for a single photograph. There are 15 family members, and 15^2= 225 different ways. Mr F says: Incorrect. It's 15! ways.

    66. Music: The window of a music store has eight stands in a fixed position where instruments can be displayed. In how many ways can three identical guitars, two identical keyboards, and three identical violins be displayed?

    I used the fundamental counting principal, and got 18. 3*2*3=18 But I know that's not right because the instruments are identical, it's not like they're different. Is the answer 3? Mr F says: No. The answer is {\color{red} \frac{8!}{3! \cdot 2! \cdot 3!}}.


    Thank you very much
    Isabel
    ..
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