1. ## simple probability question

In Tasmania, a car license consists of two letters followed by four digits. Find how many of these are possible if the second letter is X and the third digit is 3.

Thanks

2. ## Re: simple probability question

we havent done probability in our school and i have no idea of the method but ill give it a go!

for letters its 26....then for numbers there are three digits that can change so 9 in each...so 26 x 9 x 9= 2106

NOTE- this is complete guess and i would recommend to check it with an experienced person...

EDIT- its 10 for each not 9....so 26 x 10 x 10= 2600

3. ## Re: simple probability question

yeh I got 2600 but answers at the back of the cambridge textbook say 26000...

4. ## Re: simple probability question

two letters and four digits so first like theres 25 possible ways second one is already chosen
first digit theres 9 second 8 third already chosen and fourth 7

so 25*9*8*7 = 12600

i assume the digits are 0-9 LOL at me :L

wait you didnt mention if they repeat or not?

5. ## Re: simple probability question

Originally Posted by bleakarcher
yeh I got 2600 but answers at the back of the cambridge textbook say 26000...
i am total idiot...its 26..and 10 each for three digits...so 26 x 10 x 10 x 10= 26000 there u go

6. ## Re: simple probability question

Originally Posted by bleakarcher
In Tasmania, a car license consists of two letters followed by four digits. Find how many of these are possible if the second letter is X and the third digit is 3.

Thanks
Alright so first of all there has to be two letter and the second letter has to be X so its 26 x 1 right? which is just 26, then there are only 3 digits that can be used in the licence plate so 26 x 10^3 = 26000.

God, I love perms and combs.

7. ## Re: simple probability question

Wouldnt the solution just be 26 * 10*10*10 = 26000?

8. ## Re: simple probability question

Originally Posted by bleakarcher
In Tasmania, a car license consists of two letters followed by four digits. Find how many of these are possible if the second letter is X and the third digit is 3.

Thanks
LX DD3D

L = Letter
D = Digit.

First Letter has 26 options.

First Digit has 10 options.

Second Digit has 10 options.

Last Digit has 10 options.

26 x 10 x 10 x 10 = 26000

9. ## Re: simple probability question

you should include "repetition allowed in your question next time"

10. ## Re: simple probability question

Originally Posted by bleakarcher
yeh I got 2600 but answers at the back of the cambridge textbook say 26000...
It is 26000, Letters in alphabet is 26, and there are 10 digits. a car license consists of two letters followed by four digits

Find how many of these are possible if the second letter is X and the third digit is 3. Since one letter and a digit is chosen we are left with

26 * 10 * 10 * 10 = 26000

11. ## Re: simple probability question

Isn't the third digit fixed though?

12. ## Re: simple probability question

Originally Posted by zeebobDD
you should include "repetition allowed in your question next time"
Usually the question will state if there IS NOT repetition. If there is nothing stated you usually would just assume it's allowed because it doesn't say it isn't.

13. ## Re: simple probability question

Originally Posted by Timske
It is 26000, Letters in alphabet is 26, and there are 10 digits. a car license consists of two letters followed by four digits

Find how many of these are possible if the second letter is X and the third digit is 3. Since one letter and a digit is chosen we are left with

26 * 10 * 10 * 10 = 26000
OMGGGGGGZZZZZZZZZZZZZZZZZZZZZZZZ

My mind told me that there were 3 digits for some reason..

Alright thanks guys.

14. ## Re: simple probability question

Originally Posted by bleakarcher
Isn't the third digit fixed though?
yeah but theres 4 digits, so thers 3 digits left

15. ## Re: simple probability question

Originally Posted by bleakarcher
Isn't the third digit fixed though?
It's a 4 digit number plate, the last number has to be 3, so that's 1 possible combination followed by 10^3

16. ## Re: simple probability question

Originally Posted by bleakarcher
OMGGGGGGZZZZZZZZZZZZZZZZZZZZZZZZ

My mind told me that there were 3 digits for some reason..

Alright thanks guys.

I make mistakes like that all the time!

17. ## Re: simple probability question

If there were no restrictions, it would be 26 x 26 x 10 x 10 x 10 x 10
But one letter slot is taken up and one number slot is taken up, so you ignore them.
It now becomes 26 x 10 x 10 x 10 = 26000
Or in the permutation format (nPr) which you would use the calculator for: 26P1 x 10P1 x 10P1 x 10P1 = 26000
n = number of objects available
r = the amount needed to be chosen

Pretty much what everyone has said before XD

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