Can someone show me how to do this math problem?

[alexjohnson16]

How many three - letter and three - digit license plates can be made if no digits can be repeated?

I have no clue how to do this. I know it involves factorials, but I just don't know how to get this done.

 

[b0mbrman]

Originally posted by: alexjohnson16
How many three - letter and three - digit license plates can be made if no digits can be repeated?

I have no clue how to do this. I know it involves factorials, but I just don't know how to get this done.

26 x 25 x 24 x 10 x 9 x 8 x 1 x 2 x 3 x 4 x 5 x 6

booya!

[Edit] Guess I didn't do much showing

 

[MartyMcFly3]

26 letters in the alphabet.
10 numbers (0-9).

No repeats.

So you have 26 options for letter A. 25 options for letter B. 24 options for letter C.
And you also have 10 options for number A. 9 options for number B. 8 options for number C.

26*25*24*10*9*8 = 11,232,000 possible combinations.

 

[bleeb]

(Letter)(Letter-1)(Letter-2)(Digit)(Digit-1)(Digit-2)
26*25*24*10*9*8

 

[Inspector Jihad]

Originally posted by: b0mbrman

Originally posted by: alexjohnson16
How many three - letter and three - digit license plates can be made if no digits can be repeated?

I have no clue how to do this. I know it involves factorials, but I just don't know how to get this done.

26 x 25 x 24 x 10 x 9 x 8 x 1 x 2 x 3 x 4 x 5 x 6

booya!

ka sha

 

[Legendary]

No repeats for just digits, but repeatable letters?
(26^3)*(10*9*8)

 

[Brackis]

Out of curiosity for a cobwebbed mind...does this come out to be a simple combination/permutation?

 

[alexjohnson16]

Why does it go from 10-8 than 1-6?

 

[her209]

Wouldn't it be?

26*26*26*10*9*8

 

[b0mbrman]

Originally posted by: MartyMcFly3
26 letters in the alphabet.
10 numbers (0-9).

No repeats.

So you have 26 options for letter A. 25 options for letter B. 24 options for letter C.
And you also have 10 options for number A. 9 options for number B. 8 options for number C.

26*25*24*10*9*8 = 11,232,000 possible combinations.

Don't forget to shuffle up the numbers and letters once you have them selected

 

[So]

if letters and numbers CAN be repeated:
26^3*10^3
if letters CANNOT be repeated and numbers CAN be repeated:
26*25*24*10^3
if letters CAN be repeated and numbers CANNOT be repeated:
26^3*10*9*8
if neither letters nor numbers can be repeated:
26*25*24*10*9*8

 

[MartyMcFly3]

Originally posted by: b0mbrman

Originally posted by: MartyMcFly3
26 letters in the alphabet.
10 numbers (0-9).

No repeats.

So you have 26 options for letter A. 25 options for letter B. 24 options for letter C.
And you also have 10 options for number A. 9 options for number B. 8 options for number C.

26*25*24*10*9*8 = 11,232,000 possible combinations.

Don't forget to shuffle up the numbers and letters once you have them selected

Good point. If its just 3 letters then 3 numbers then it's good though. OP left out some details.

 

[bleeb]

Originally posted by: So
if letters and numbers CAN be repeated:
26^3*10^3
if letters CANNOT be repeated and numbers CAN be repeated:
26*25*24*10^3
if letters CAN be repeated and numbers CANNOT be repeated:
26^3*10*9*8
if neither letters nor numbers can be repeated:
26*25*24*10*9*8

you OWN this problem. good job!

 

[hypn0tik]

26*25*24*10*9*8 (Edit: Assuming of course, neither letters nor numbers can be repeated).

That's ONLY to pick all the letters and number. Now, within the 6 you pick, they can be arranged in 6! ways to give you unique license plates. Hence, you have:

26*25*24*10*9*8*6!

 

[her209]

Wouldn't some permutation of letters be counted multiple times, e.g. AAA123?

 

[shira]

Just realized. This has to be broken into three cases:

Three different letters: 26*25*24*10*9*8*6!

Two different letters: 26*1*25*10*9*8*6!/2!

All letters the same: 26*1*1*10*9*8*6!/3!


Total license plates is the sum of those three values.

 

[alexjohnson16]

Argh, everyone's answer is different.

I wish I had this actual class instead of online, its more difficult to learn on the internet.

 

[Vegitto]

Well, it depends. Is AAA123 = A123AA?

 

[shira]

Originally posted by: Vegitto
Well, it depends. Is AAA123 = A123AA?

Obviously not. These are not the same license plate.

 

[eelw]

Originally posted by: Vegitto
A123AA?

Is that even a valid plate? And there would be even more combinations here in Ontario since we have 4 letter and 3 number plates.