a lock has a 4 digit combination where no number can be repeated how many possible combinations are there​

Question

a lock has a 4 digit combination where no number can be repeated how many possible combinations are there​

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Thu Thảo 4 years 2021-07-30T22:58:15+00:00 1 Answers 9 views 0

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  1. kimchi2
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    2021-07-30T22:59:53+00:00
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    Answer:

    4,536

    Step-by-step explanation:

    Ok so lets write down any old 4 digit number

    abcd

    How many choices do we have for the digit a? We have 9 choices (since the first digit cannot be 0). Now for each possible choice of a we have 9 choices for b (since we want b to be a different digit to a and we now allow 0).

    So for choice of the ab part we have 9∗9=81 possibilities.

    Now for each of these we have 8 choices for c (to avoid c being the same as either a or b). And for each of these we have 7 choices for d (to avoid d being the same as either a,b or c).

    So in total there are 9∗9∗8∗7=4536 possible numbers.

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