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Math Help - Where to use the power principle.

  1. #1
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    Where to use the power principle.

    I know when and where to use the multiplication principle.
    "If one operation can be performed in r different ways and another operation can be performed in s different ways, then the number of different ways in which the two combined operations can be performed is r ! s."
    Can someone tell me where should I use the power principle (I don't know what is actually its name 2^3, 2^8 etc) and also the factorial (2!, 5! etc)

    CB
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by computer-bot View Post
    I know when and where to use the multiplication principle.
    "If one operation can be performed in r different ways and another operation can be performed in s different ways, then the number of different ways in which the two combined operations can be performed is r ! s."
    Can someone tell me where should I use the power principle (I don't know what is actually its name 2^3, 2^8 etc) and also the factorial (2!, 5! etc)

    CB
    i googled the multiplication principle and it actually has nothing to do with the definition you stated. i googled the power principle and didn't find anything pertaining to the definition stated either. so can you give us an example of where you used these principles in class?

    secondly, are you sure it is "r ! s" and not "r*s"?
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  3. #3
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    Quote Originally Posted by computer-bot View Post
    I know when and where to use the multiplication principle.
    "If one operation can be performed in r different ways and another operation can be performed in s different ways, then the number of different ways in which the two combined operations can be performed is r ! s."
    Can someone tell me where should I use the power principle (I don't know what is actually its name 2^3, 2^8 etc) and also the factorial (2!, 5! etc)

    CB
    They are the same thing. If one operation can be performed in r ways
    and the second is s ways, then for each of the r ways there are for the
    first operation there are s ways to do the second so we have r*s ways
    altogether.

    Now if there are n operations and a_1, a_2, .., a_n ways of doing each of
    these then there are:

    A=a_1*a_2*..*a_n

    ways of doing the combined opeartions.

    Now if all the a_i's are equal to a say, we have:

    A=a^n.

    The other common form is that a_i = n-(i+1), then:

    A=n!

    RonL
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    Quote Originally Posted by Jhevon View Post
    i googled the multiplication principle and it actually has nothing to do with the definition you stated.
    I have allached a file. Go to page 5 of this file and you'll find this definition. I found it on Google.
    File

    Quote Originally Posted by Jhevon View Post
    i googled the power principle and didn't find anything pertaining to the definition stated either.
    I never gave any definition for power.
    Quote Originally Posted by Jhevon View Post
    so can you give us an example of where you used these principles in class?
    Well as I said, I am not familiar with the jargon so I don't know what this principle/rule/method is actually called. But to elaborate what I needed, consider the following example;
    Each time a coin is flipped there are two possible outcomes, head and tails. If an experiment consists of 8 consecutive coin flips, then the experiment has 2^8 possible outcomes, where each of these outcomes is a list of heads and tails in some order.


    Quote Originally Posted by Jhevon View Post
    secondly, are you sure it is "r ! s" and not "r*s"?
    Sorry that was my mistake. It is r*s.
    Attached Files Attached Files
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    Quote Originally Posted by CaptainBlack View Post
    They are the same thing. If one operation can be performed in r ways
    and the second is s ways, then for each of the r ways there are for the
    first operation there are s ways to do the second so we have r*s ways
    altogether.
    This is exactly what I meant.


    Quote Originally Posted by CaptainBlack View Post
    Now if there are n operations and a_1, a_2, .., a_n ways of doing each of
    these then there are:

    A=a_1*a_2*..*a_n

    ways of doing the combined opeartions.

    Now if all the a_i's are equal to a say, we have:

    A=a^n.

    The other common form is that a_i = n-(i+1), then:

    A=n!
    RonL
    Okkkkkkkkkkkkkkkkkk!!! Got it.
    This is my take. Say if there are 2 operations and each operation could be performed in 5 ways so the total number of possible outcomes will be 5*5 or 5^2. Well this is just like the multiplication rule.

    OK so let me explain this for other readers.
    When we have more that one number of operations say 3 and at least two of these operations could be performed in different number of ways then we have to the plain multiplication rule or simply multiply the number of ways of operations with each other. For example if we have 5 Math books, 5 Physics Books and 4 Chemistry Books and we have to choose a set that consist of each one of the subject then we have to multiply them i.e 5*5*4.

    But in my previous example (previous post - the coin example), we had to flip the coin 8 time (8 operations) but each time the number of way to perform it were 2 (heads or tails) therefore we have to multiply the number of possible ways for each operation (which is same in this case) 8 time (the total number of operations). The expression will be 2*2*2*2*2*2*2*2 which is equal to 2^8.

    CB
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  6. #6
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by computer-bot View Post
    This is my take. Say if there are 2 operations and each operation could be performed in 5 ways so the total number of possible outcomes will be 5*5 or 5^2. Well this is just like the multiplication rule.
    yes, 5^2 is the number of different combinations of the two operations we can perform.

    OK so let me explain this for other readers.
    that's very nice of you

    When we have more that one number of operations say 3 and at least two of these operations could be performed in different number of ways then we have to the plain multiplication rule or simply multiply the number of ways of operations with each other.
    ok, with you so far
    For example if we have 5 Math books, 5 Physics Books and 4 Chemistry Books and we have to choose a set that consist of each one of the subject then we have to multiply them i.e 5*5*4.
    ok, but you didn't really say what 5*5*4 is. this is the number of distinct sets consisting of one book from each area we can make. in other words, this tells us how many ways we can make a set consisting of one math, one physics, and one chemistry book.


    But in my previous example (previous post - the coin example), we had to flip the coin 8 time (8 operations) but each time the number of way to perform it were 2 (heads or tails) therefore we have to multiply the number of possible ways for each operation (which is same in this case) 8 time (the total number of operations). The expression will be 2*2*2*2*2*2*2*2 which is equal to 2^8.
    well, almost, but not exactly. you seem to be confusing outcomes with the different ways we can perform an operation. i guess in some instances those two would end up being the same, but not here. there's one way we can flip a coin essentially. but it has two different outcomes. heads or tails is not the operation, they are the results (or outcomes) of performing the operations. so here i think the number of operations is 8. 2^8 represents something different. in other words, i do not think we would apply the multiplication principle in this situation in the way you applied it
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  7. #7
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    Quote Originally Posted by Jhevon View Post

    well, almost, but not exactly. you seem to be confusing outcomes with the different ways we can perform an operation. i guess in some instances those two would end up being the same, but not here. there's one way we can flip a coin essentially. but it has two different outcomes. heads or tails is not the operation, they are the results (or outcomes) of performing the operations.

    Well the first example (of books) was that of multiplication principle but the second one (the coin flips) is of exponents. My point is that when we have different number of options, as in case of books where for one subject we had 5, for second we also had 5 but for third we had 4, we use multiplication principle (i.e 5*5*3) But say if we had 5 options for each one of the subjects then by multiplication principle, we had the statement 5*5*5 or in other words 5^3 which is the exponent principle (I know it's not called exponent principle but I am using this term to refer to it).
    Please correct me if I am wrong.
    Quote Originally Posted by Jhevon View Post
    so here i think the number of operations is 8. 2^8 represents something different. in other words, i do not think we would apply the multiplication principle in this situation in the way you applied it.
    Well I also said that the number of operations is 8.

    CB
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  8. #8
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    I think we can't say that 2^8 is from another principle than that of multiplication principle. it's just the matter of outcomes of operations. If each operation has the same number of outcomes then we can use the exponent.

    CB
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