Am I using the right equations? Determine the number of possible outcomes when making a 7-character license plate using the letters of the alphabet and the digits 1-4 if the first 3 characters must be non-repeating letters and the remaining 4 are digits that may repeat. 26C3 x 16C4

Question

campbell_st · Answer

so there are 26 + 4 choices... the 1st 3 without replacement

      30 x 39 x28 x 30C4

anonymous · Answer

I would think 26*25*24*4^4

campbell_st · Answer

that correct... 26 x 25x 24 x4^4

brinazarski · Answer

I'm pretty confused right now...

anonymous · Answer

Rationale for the above answer:  The first letter can be any of 26.  The next can be any of the remaining 25, the next can be any of the remaining 24.  Each of the four digits can be any of the four digits available, so those contribute a factor of 4^4.

anonymous · Answer

I get 3993600.

brinazarski · Answer

That's the right answer (have the answer key) I'm just trying to figure out how you got there... I get the 26*25*24 etc, which is why I put 26C3... or is there no etc, and it's just 26 x 25 x 24?

zarkon · Answer

$$26\cdot25\cdot24=\,_{26}P_{3}$$

brinazarski · Answer

-sigh- I'm so confused. I think I'll just leave this question for tutoring ^^;

zarkon · Answer

$$26\cdot25\cdot24\ne\,_{26}C_{3}=\frac{26\cdot25\cdot24}{3\cdot2\cdot1}$$

brinazarski · Answer

True, but why is that example a permutation?

zarkon · Answer

the order that you pick the letter matters

brinazarski · Answer

... true :o But then the numbers are C, right? (I can't remember the name of it atm, too tired, but I know what it is lol)

zarkon · Answer

for 'C' the order does not matter

brinazarski · Answer

And the numbers may repeat, so the order doesn't matter, right?

zarkon · Answer

the order does matter....

you get 4x4x4x4

brinazarski · Answer

But why...?

zarkon · Answer

why the order matters or why it is 4x4x4x4?

brinazarski · Answer

Both ^^;

zarkon · Answer

are ABC1234 and ABC4321 the same license plate?

brinazarski · Answer

No...

zarkon · Answer

so the order of the numbers matters

brinazarski · Answer

x.x... so why 4^4?

zarkon · Answer

and since you can have repeated numbers..you have 4 choices for the first number , 4 for the second, 4 for the third, and 4 for the fourth.  Thus 4x4x4x4 total

brinazarski · Answer

Ah.... that's true

brinazarski · Answer

4^4 = 4096, right?

zarkon · Answer

$$4^4=256$$

brinazarski · Answer

x_x I don't have my graphing calc, sorry. So do I do 256 x 26P3?

zarkon · Answer

put 256*26*25*24 into google

brinazarski · Answer

Mhmm... that's the answer

brinazarski · Answer

26*25*24 = 26P3, right...?

zarkon · Answer

yes

brinazarski · Answer

Okay :) Thank you so much!