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Math Help - nCr or nPr?

  1. #1
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    nCr or nPr?

    I'm reading my textbook, but i don't understand the difference between ^n\mathrm{C}_r and ^n\mathrm{P}_r? All it says that for ^n\mathrm{P}_r the order matters and for ^n\mathrm{C}_r,the order doesn't matter but i'm not sure what this means. I can do the working out etc. but I'm just worried when i come across a worded problem, i'm not sure which one to apply?

    if anyone can explain, il be super grateful!
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  2. #2
    Pim
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    Well, it exactly is as your textbook says: Does order matter or not?

    If you get a question about differently coloured cars arranged in different ways, order matters. Ways of seating people is another common one. Therefore, for both you use ^n\mathrm{P}_r<br />
    Combinations are used when order does not matter. In how many different ways can you choose a committee consisting of 3 people from 25 students? ^{25}\mathrm{C}_3

    Does this make it any clearer?
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  3. #3
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    Quote Originally Posted by chinkmeista View Post
    I'm reading my textbook, but i don't understand the difference between ^n\mathrm{C}_r and ^n\mathrm{P}_r? All it says that for ^n\mathrm{P}_r the order matters and for ^n\mathrm{C}_r,the order doesn't matter but i'm not sure what this means. I can do the working out etc. but I'm just worried when i come across a worded problem, i'm not sure which one to apply?

    if anyone can explain, il be super grateful!
    Hi chinkmeista,

    Here is an example:

    We need to choose 3 officers out of 8 members in an organization (perhaps to share the work load together). How many ways can we do this?

    This is going to be a problem using combination since we are picking 3 while there is no difference which person get pick first, since 3 positions are the same. (Order does not matter)

    Thus there is ^8\mathrm{C}_3 ways.

    On the other hand, if the problem is instead:
    We need to choose 3 officers out of 8 members, a president, a secretary, and a treasurer, in an organization. How many ways can we do this?

    This is going to be a problem using permutation since we are picking 3 while there is a difference which person is the president, or the secretary, and so forth. (Order does matter)

    Thus there is ^8\mathrm{P}_3 ways.

    Does this make sense?
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  4. #4
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    Yeah a little bit thanks, just have to try my best to understand the wording of the question!
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