Exchanging Numbers and Letters

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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:

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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: