Question

A valid license plate in Xanadu consists of two capital letters followed by three digits. How many valid license plates are possible

1. The  valid license plates are possible = 676,000 possibilities

### What is permutation and combination?

In mathematics, there are two alternative methods for dividing up a collection of components into subsets: combination and permutation. The subset’s components can be arranged in any sequence when used together. The subset’s components are given in a permutation in a certain order.

### According to the given information:

There is no prohibition on using the same letters or numbers more than once, therefore all 26 letters of the alphabet and all 10 numerals are permissible choices.
There are 26 options if the initial answer is A:
AA, AB, AC,AD,AE ……………………………….. AW, AX, AY, AZ.
There are 26 options if the initial answer is B:
BA, BB, BC, BD, BE …………………………………..BW, BX,BY,BZ
So,
The first letter can be one of 26 options, and the second letter can be one of 26 options. There are a variety of 2 letter combinations, including:
26 x 26 = 676
For the three digits, the same holds true.
The first, second, and third options each have ten options available:
10  × 10 × 10 = 1000
Thus, there are several options for a license plate with two letters and three digits:
26 x 26 x 10  × 10 × 10 =  676,000 possibilities.
The  valid license plates are possible = 676,000 possibilities.
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