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Math Help - [SOLVED] finding the possible PIN codes

  1. #1
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    Exclamation [SOLVED] finding the possible PIN codes

    In a bank, it doesn't issue the PIN code with more than 2 consecutive digits the same.(For example, 7666 and 2222 are not allow but 0040 is allowed)
    i)how many different PIN codes are possible?
    ii)how many different PIN codes have 8 as their first digits?
    I don't really know how to solve this question, is there a easy way to solve it? can anyone helped me?Thank you very much!!
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  2. #2
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    Quote Originally Posted by taipei166 View Post
    In a bank, it doesn't issue the PIN code with more than 2 consecutive digits the same.(For example, 7666 and 2222 are not allow but 0040 is allowed)
    i)how many different PIN codes are possible?
    ii)how many different PIN codes have 8 as their first digits?
    I don't really know how to solve this question, is there a easy way to solve it? can anyone helped me?Thank you very much!!
    Hi taipei,

    i) If there were no restrictions, the number of possible PIN codes would be 10^4.

    The invalid codes come in 3 forms.

    Codes like xxxy: There are 10 ways to choose x and then there are 9 ways to choose y, so there are 10 \times 9 possibilities.

    Codes like yxxx: Similarly, there are 10 \times 9 possibilities.

    Codes like xxxx: There are 10 of these.

    So the number of allowable codes is 10^4 - 2 \times 10 \times 9 - 10.

    Maybe you can work out ii) from this.
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  3. #3
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    Thanks for your solution, it is really helpful!
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