The tutor offers a solution to a textbook question about counting.

On page 47 of my text Discrete and Combinatorial Mathematics (Grimaldi) is a question:

If you want to select three distinct letters from the alphabet , arranged in alphabetical order, how many ways can it be done?

The answer I’m offering is 26C3. Here’s my reasoning: let’s imagine you select P,Q, and A. They’re not in alphabetical order, but as a combination, the order doesn’t matter. Therefore, I can rearrange them to A,P,Q, and it’s still the same combination.

There are 26C3 combinations of three distinct letters from the alphabet. Since combinations are careless of order, you can arrange each combination to alphabetical order:)

Source:

Grimaldi, Ralph P. Discrete and Combinatorial Mathematics. Don Mills: Addison-
  Wesley, 1994.

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