6-key sequences possible in 6x6 grid

Question

Let's say we have a $6\times6$ panel of buttons. A user must press a sequence of any $6$ buttons, without repeating a button.

How many different ways are there to press a sequence of $6$ different buttons in this grid?

My instinct told me this is $6\times 36!$. Then Google told me it was $P(36,6)$ or $1402410240 (\sim1.4\text{ billion})$.

Is this correct?

Answer 1

Google is correct. The reason is the following:

You can imagine that each button that you pick is numbered, $1$ through $36$. For your first button choice, you have $36$ options to choose from. Then, for the next button, you have $35$ options, since you eliminated one of them from your first pick. You repeat this process a total of $6$ times, which gives you the number of permutations:

$$36\times 35\times 34\times 33\times 32\times 31=36P6=\frac{36!}{(36-6)!}$$

which gives you the roughly $1.4\times 10^9$, or $1.4$ billion you were talking about.

Answer 2

Google is correct(1402410240) You only need to choose six buttons,so you don’t need to multiple 36 factorial.(36 factorial for pressing all 36 buttons.