Permutation 6 letter password lowercase and digits?

Question

I got this question from a past exam paper.

I know there is a typo I think it is anyway where it says six letter passwords

Question

How many six letter passwords can be formed from a scheme where only lower case letters or digits are allowed, with no repetition and a password may not start with a digit?

Now because there is 26 letters and 10 digits the total is 36 characters.

But the password can not start with a digit so here was my solution

26*35*34 ......

As 26 letters can be picked for the first character and as there is no repetition that leaves 35 as a letter was entered in for the first character.

Is this the right way of approaching this problem, also is the a faster way of doing this on the calculator like using ! or P??

Answer 1

That approach seems very reasonable to me.

As to calculator tactics, note that what you have is very close to being $_{36}P_6$. Except the first $36$ is instead $26$. So if I had to use built-in functions, I would enter it as $26\cdot{}_{35}P_5$ (whether this actually saves any time compared to typing out the entire product is not completely clear to me, but if you wanted, say, 15 character passwords then you would start to see some significant gains from this).