SOLUTION: There is a box with a padlock You can open the box if you will be able to know the 4-digit code in the padlock. If the first digit of the 4-digit code is 5, how many possible codes
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Question 1193059: There is a box with a padlock You can open the box if you will be able to know the 4-digit code in the padlock. If the first digit of the 4-digit code is 5, how many possible codes are there if the repetition of the digit code is allowed?
You can put this solution on YOUR website! there is one possible digit for the first position and 9 possible digits each for the next 3 digits.
the number of possible combinations is 1 * 9 * 9 * 9 = 9^3 = 729.
to understand how this works, assume there are only 2 possible digits for the next 3 positions.
the number of possible combinations would then be 1 * 2 * 2 * 2 = 2^3 = 8.
assuming the 2 possible numbers for each position were 2 and 3, then you would get:
5222
5223
5232
5233
5322
5323
5332
5333
the same concept applies when there are 9 possible numbers for each digit, except the number of combinations are too numerous to individually display.
Of 4 possible digit positions, the first position is just occupied by the digit of 5.
Three other positions are free, and we can put any of 10 possible digits from 0 to 9 in any of these 3 positions.
It gives = 1000 possible digit codes. ANSWER
Solved (correctly).
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Ignore answer by @Theo, since it is INCORRECT.
I don't know why @Theo decided about 9 digits.
Working base 10, we always have 10 possible digits.
