Math CentralQuandaries & Queries


Question from Edward:

I have a inline lock with four rows of numbers 0-9.The numbers cannot be repeated.
Can you please print the possible codes so I can go through them one at a time. The
lock and the cable cost $\$300.$ Don't want to pitch it. You guys are lifesavers, can't
wait to hear back. Thanks.

Hi Edward,

You have 10 choices for the digit in the first row and once you have chosen it you have 9 digits to choose from for the second row. Once these two are chosen you have 8 choices for the third row and so on. Since you have 4 rows there are $10 \times 9 \times 8 \times 7 = 5040$ possible codes.

To list them you can use a tool on the Math Is Fun site. Set n = 10, r = 4, toggle is repetition allowed? to no and you will get 5040 as the number of permutations. To obtain a list, in the List Them box type 0 to 9, separated by commas and select list.

Good luck in getting it open,

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