In how many 4th permutations of given subset $a$ and $b$ are adjacent?

Question

Suppose we are given that

$$K = \{a,b,c,d,e,f\}$$

In how many 4th permutations of given subset $a$ and $b$ are adjacent?

So we have four choices for remaining letters when we put $a$ and $b$

$$ab\_\space \_$$

Now let us pick 2 letters out of 4 letters, which can be done in $\binom{4}{2}$ ways. However, $a$ and $b$ have to be together so we can consider them as an object yielding $3!$ Thereby, we finally have that

$$\binom{4}{2}3! = 6^2 = 36$$

Am I right?

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