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| Math Central | Quandaries & Queries |
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Question from cheri, a parent: COULD YOU GIVE ME ALL THE # COMBINATIONS I NEED 3 DIGIT NUMBERS MADE OUT OF THE NUMBERS 1, 2, 3, 0.. I CAN OLY COME UP WITH.. IM TRYING TO MAKE PASSWORDS FOR MY FINGERPRINT LOCK I PURCHASED, AND THEY TOLD ME THEAR I COULD GET 78 DIFF COMBOS,,,,, PLEASE HELP ASAP, NEED TO GET MY CUSTOMERS HOOKED UP SO THAT THEY CAN ENTER THE CLUB HELP AND THANK YOU SO SO MUCH |
Hi Cheri,
I don't know where 78 might have come from.
If no digit can be repeated, then the first number can be any of the four, the second number any of the remaining three, and the third number any of the remaining two. That means that, in this case, number of combinations is 4x3x2 = 24.
If digits can be repeated then a similar calculation shows that the number is 4x4x4=64.
Other cases (e.g. the first digit can't be zero and no two consecutive digits can be the same) can be analyzed similarly.
Victoria
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