Perms and Combs Serial Number Question (1 Viewer)

[KaoticKreature]

Hey guys, I was just going though some Perms and Combs questions for my exam tomorrow and I came across this question:

A serial number is made up of 4 letters and 2 numbers. If zero is not allowed, find how many serial numbers are possible.

Now, the answers say that it is 37015056 which is what you get if you do 26^4 x 9^2. But here's the issue; shouldn't u then have to multiply it by 6! since you have to arrange the numbers and letters in 6! ways? How come this doesn't give the answer?

Thanks guys!

 

[parad0xica]

Serial number: an identification number showing the position of a printed or manufactured item in a series. (retrieved from Google)

This implies the order of the letters and numbers matter, so we don't multiply by 6!.

 

[dannyphm]

Hold on. If order matters then isn't multiplying my 6! necessary to account for the 6 factorials in which you could arrange every unique serial arrangement?

 

[Ambility]

The question must be meaning a serial number which has 4 letters, followed by 2 numbers, in that order. There would be more combinations than 37015056 if the serial numbers allowed letters and numbers to be in any order. This is what I don't like about permutations and combinations, the questions often don't sufficiently provide explicit information to answer them.

 

[parad0xica]

Hold on. If order matters then isn't multiplying my 6! necessary to account for the 6 factorials in which you could arrange every unique serial arrangement?

If you arrange it, then order is not preserved.

The structure of this serial number must be this:

L L L L N N​

where L = letter and N = number.

Suppose we arrange it (one arrangement method out of 6! possible arrangements) such that it yields the following:

N L L L L N​

We see order is not preserved and hence we should not multiply the result by 6!.