Number of straight flushes and three-of-a-kinda with three cards

Question

The two questions involve drawing 3 card combinations (thus non-repeating) from a standard 52-card deck with the following conditions.

1. 3 cards in a "ladder-type" ascending order from the same suit (e.g. A23 of spades, QKA of hearts)
2. 3 cards with the same value (e.g. 111, QQQ)

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For the first question, I could solve it by listing all ascending groups possible within a certain suit:

A23, 234, 345, (...), QKA, KA2. (13 combinations)

And then multiplying by the number of suits: 13 x 4 = 52 combinations

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For the second question, I could solve it by listing all values:

A, 2, 3, (...), J, Q, K. (13 values)

And then multiplying them by 4C3 (as every 3 card combination chooses 3 cards with a specific value from 4 of such cards possible): 13 x 4C3 = 52 combinations

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First of all, I would like to know if my answers are correct. And then, if possible, if there are any other approaches to these problems that perhaps use more combinatorics notation. This are some questions I raise in my IB math SL investigation, and I feel that just listing values/combinations doesn't really show I'm confident with exploring combinatorics.

Thanks in advance!

Answer 1

Your answers seem fine to me, except that the problem poser may not think of KA2 as a straight, or allow both QKA and A23.

Given your understanding of what constitutes a straight, though, an alternative approach to both problems is to note that each straight flush can be identified by its starting card, while each three of a kind can be identified by the fourth card of the same value, so the answer for each problem is simply $52$. That is, pick any card, which can be done in $52$ ways, and then complete it (upward) to a straight flush for the first problem, or replace it with the other three cards of the same value for the second problem.