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Re: A local bank that has 15 branches uses a two-digit code to
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21 Feb 2022, 10:47
It is required to deliver 15 two-digit codes, in such a way that the different arrangements that can be made with 2 digits (a code) must be considered all, an example 21 and 12 are different codes, in addition the same number can be repeated to generate a code. Attention, the least number of digits possible is requested.
Given that 21 and 12 are different codes and this will happen for each two-digit number, the approximation to the proposed situation leads us to consider a permutation and not a combination.
The model will be:
(kPn + k) greater than or equal to 15, lower value of n.
Note kPn + k = n!/(n-k)! + k = kexp2
We look for the minimum k possible (minimum number of digits, to generate 15 two-digit codes, (permutation, we already explained why) (kPn), we must also consider that the digits can be the same, if I choose k digits we will have (k) pairs same.
Let's start playing:
If we consider A) 3, 3 digits from which to choose to form the two-digit numbers, we have:
(2P3 + 3) = 3!/(3-2)! + 3 = 3! + 3 = 9 = 3exp2, we don't get to 15 or more.
If we consider B)4, 4 digits from which to choose to form the two-digit numbers, we have:
(2P4 + 4 ) = 4!/(4-2)! + 4 = 4x3 + 4 = 16 = 4exp2, we arrive at 15 +1.
Then the minimum number of digits necessary to generate the two-digit codes in the indicated terms is: 4
Answer B