Probability of drawing two cards such that one is a spade and other one is a heart.

For the first formula, order is taken into account. We are counting ordered pairs of cards. If you don't multiply by $2$ you'll miss the drawing in the opposite order.

For the second one we are counting sets, where order does not matter. Exchanging the two elements of the set changes nothing, so if you multiply by two you'll get the wrong answer.


Let me suggest another way to solve the problem that might help you think about it. You have $26$ choices out of $52$ of a first card that keeps you "alive." After choosing that first card, you have $13$ choices out of $51$ of a second card that keeps you alive.

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Combinatorics

Probability

Permutations

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