Question

Automobile license plates for a state consist of four letters followed by a dash and two single digits. How many different license plate combinations are possible if exactly one letter is repeated exactly once, but digits cannot be repeated

1. kimchi2
The number of different license plate combinations that are possible if exactly one letter is repeated exactly once, but digits cannot be repeated is 8,424,000.

### What is combination?

A combination is just a mathematical technique for determining the number of potential arrangements in a set of objects where the order of a selection is irrelevant.
You can choose the components in any order in combinations. Permutations and combinations are often mistaken.
Now according to the question,
Possible letter combinations
Choose any letter and make it a repeat letter = 26 ways
But, there are ⁴C₂ = 6 spots available for the identical letters.
And there are (25)×(24) other methods for selecting the other two letters.
The total amount of “words” equals ⁴C₂ × 26 × 25 × 24 = 93600.
Furthermore, because the numerals cannot be repeated = 10 × 9 = 90
So, the total number of choices = 93600 × 90 = 8,424,000
Therefore, the total combinations in which the letters can be chosen for the license plates is  8,424,000.
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