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Can someone please help me with my permutations / combinations problem?

  • 04-02-2018 9:37pm
    #1
    Franciskus Gayelord Petulah 18
    Site Banned Posts: 43 ✭


    It's not homework help, I'm almost 27 :P I just can't get my head around this one.


    Problem:

    You have been asked to make a password from a standard Euro/Us keyboard. It must be exactly 7 characters long and can only contain upper or lower case letters and numbers or their corresponding symbols (for example 5 or %) and no character can be repeated.

    The solution to this is:

    Since there are 26 letters (52 in total if you include upper and lower case) and 10 numbers (20 if you include their corresponding symbols), that gives us 72 characters to work with.

    So the possible combinations are 72*71*70*69*68*67*66=7,424,472,908,160 combinations.

    The second part of this problem is that one I can't solve.

    The problem:

    The criteria for the password has changed. The password must be a minimum of 7 characters and a maximum of 14 characters, using the same character rules, how many combinations are possible?

    Do we simply solve all of the combinations for the above using n=7,8,9......14 and multiply all of the results?

    Would that give us the correct answer or is there a quicker was to do it?

    Am I right in calling that a combination or is that a permutation?


Comments

  • #2
    MathsManiac
    Registered Users, Registered Users 2 Posts: 1,595 ✭✭✭MathsManiac


    Franciskus Gayelord Petulah 18 wrote: »
    ...
    Do we simply solve all of the combinations for the above using n=7,8,9......14 and multiply all of the results?

    Would that give us the correct answer or is there a quicker was to do it?

    Nearly right. You work them out and add them. If you think about it, you should be able to satisfy yourself as to why. Bear in mind that the password has to have 7 characters OR 8 characters OR 9 characters OR etc.
    Franciskus Gayelord Petulah 18 wrote: »
    ...
    Am I right in calling that a combination or is that a permutation?
    Each possible code is a permutation, because the order the characters are in matters. If the task was to just choose 7 characters from 72, (where the order therefore wouldn't matter,) that would be a combination.

    By the way, on a scientific calculator, you can get 72*71*70*69*68*67*66 using the "nPr" key (P for permutation), so you'd key in 72[nPr]7[=].

    And finally, as I'm a bit of a pedant...
    Franciskus Gayelord Petulah 18 wrote: »
    The criteria for the password has changed.
    That should be: "The criteria have changed" or "The criterion has changed". Criteria is plural, the singular of which is criterion. I rail against the incresing commonality of this grammatical error!
    ;)


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