## JorgeG 3 years ago A license plate is identified by a string of two letters followed by five numbers. If each license plate is distinct, find the number of possible license plates. Answer 39,917,124 9,828,000 67,600,000 19,656,000

1. JorgeG

@Kira_Yamato

2. Kira_Yamato

Is repetition of digits and alphabets allowed?

3. JorgeG

only repettiton of digits only 8 digits to be sure..

4. Kira_Yamato

Circles = space for letters Square = space for digits Numbers = no. of ways|dw:1352605436090:dw|

5. JorgeG

squares

6. JorgeG

@rahul91 can you help?

7. JorgeG

is it 39,917,124?

8. JorgeG

@Study23 I need help with my question...

9. rahul91

you have 7 positions . first two for alphabets right ,since each plates are different you have to solve this problem as for a non repetitive case .. are you OK this far

10. Study23

$$\ \large \text{ This is a problem involving permuations...}$$ $$\ \large \text{So the first two places of the plate are letters.There are 26 letters.}$$ $$\ \large \text{So the first place could have} \frac{1}{26} \text{letters}$$.

11. Study23

So there are a possible 26 letters for the first digit, right?

12. Study23

Are you allowed to repeat the same number/letter?

13. JorgeG

Yes 26 letters for the first digit and yes allowed to repeat same number

14. JorgeG

15. Kira_Yamato

For the letters, You can have 26^2 = 676 ways of arranging. For numbers, You can have 10^5 = 10000 ways Multiply them and you get 676 00000

16. JorgeG

Thanks I got it! (: