Everyone must have a birth certificate or identity card. The CPF and voter registration card are also essential documents for any citizen. All these documents have the person's name and an identification number that facilitates access to each civilian's registration information.
The vehicles also have a register with various information about color, model, year, chassis number, engine number, power, owner, location address, among others. Access to these registration data is carried out through the vehicle identification plate.
Previously, plates were formed by a combination of two letters and four numbers. Considering that the alphabet is composed of 26 letters and our numbering system consists of 10 digits, the possible permutations were given by:
26 * 26 * 10 * 10 * 10 * 10= 6.760.000
In each column of letters we have the option of 26 letters and, in the case of numbers, the option of 10 digits.
As the number of cars increases over the years, the departments responsible for registration of cars in circulation decided to adopt the presence of one more letter on the license plates of the automobiles. This measure increased the number of combination possibilities. Watch:
26 * 26 * 26 * 10 * 10 * 10 * 10 = 175.760.000
The calculations presented provide all possible permutations, including those involving identifications of the same letters and numbers. For example:
YYY - 0000
PPP - 1111
TTT - 8888
XXX - 4444
If it is necessary to calculate the number of permutations only of plates with distinct elements, we must adopt the following mathematical calculation:
26 * 25 * 24 * 10 * 9 * 8 * 7 = 78.624.000
Examples:
ABC – 1234
JDT - 8547
PTA - 1238
TDX - 5621
Some other restrictions can be used in the elaboration of the boards. Look:
Only the distinct letters
26 * 25 * 24 * 10 * 10 * 10 * 10 = 156.000.000
Examples:
ABC - 2255
PDR - 8888
XTA - 8787
NKS - 9025
Only the distinct numbers
26 * 26 * 26 * 10 * 9 * 8 * 7 = 88.583.040
Examples
AAP – 1258
BBV - 8742
LKL - 5468
HIJ - 7236
by Mark Noah
Graduated in Mathematics
Brazil School Team
Combinatorial Analysis - Math - Brazil School
Source: Brazil School - https://brasilescola.uol.com.br/matematica/permutando-numeros-letras.htm