# 5 cards are drawn one at a time without replacement from a deck of 52.

Calculate the probability of landing a straight flush. A royal flush is considered a straight flush.

I can't be sure, but I think the answer changes depending on the first card you choose. Like if you choose an Ace, the Ace can only start or end the flush while the card '6,' for example, can be in the middle or the start or the end of a flush (thus giving more possibilities for future choices)

Your doubt is about another question: "What is the probability of landing a straight flush if the first card is 6?". This is a different question and has a different answer.

A straight flush starts with card of rank A, 2, 3, 4, 5, 6, 7, 8, 9 or 10 and can be of any suit so the total number of straight flushes is 40. In total there are $\binom{52}{5} = 2598960$ possible hands, so the probability of getting a straight flush is ${40\over 2598960}={1\over 64974}$.

Probability of a straight flush including royal flush will be

Including J, Q and K there are $13\cdot4 = 52$ straight flushes

$$(10\cdot4) / \binom{52}{5}$$

Excluding J, Q and K there are $10 \cdot 4 = 40$ such combinations. Like $\{A, 2, 3, 4, 5\}, \{2, 3, 4, 5, 6\}\cdots$etc.

$$(13\cdot4) / \binom{52}{5}$$