License Plates

Probability Level 2

In Brazil, the car license plates are composed of 3 letters (A-Z), and 4 numbers (0-9) not necessarily distincts (look the image above). How many car plates can be formed with this property?

The alphabet have 26 letters.

The answer is 175760000.

3 solutions

Rohit Sachdeva
Sep 8, 2014

Each of the 3 alphabet place has 26 options(A-Z)

Each of the 4 digit place has 10 options(0-9)

Hence total number of ways is:

(26 x 26 x 26) x (10 x 10 x 10 x 10)

= $\boxed{175760000}$

how can we take 10 in thousand's place,because 0 can't take into account ie to make a four digit number we can take only 1-9 numbers only and no 0 so I propose the answer as (26 26 26) (9 10 10 10) = 158184000

Sai Siddhu - 6 years, 8 months ago

The problem with that logic is that the problem says four numbers (0-9) not a four digit real number.

Stephen Hanna - 6 years, 7 months ago

0000 number numberplate not valid so....10×10×10×10—1=9999 So 26×26×26×9999=175742424

Heet Bhimani - 6 years, 5 months ago

0000 number numberplate not valid so....10×10×10×10—1=9999 So 26×26×26×9999=175742424

Heet Bhimani - 6 years, 5 months ago

There is $0000$ car numberplate really exists.

. . - 3 months, 3 weeks ago

Thomas O'Brien
Jan 4, 2015

There are three positions which the 26 letters of the alphabet can be in, so 26^3=17576. And there are 4 positions for the ten letters to be in, so 10^4=10000. You then times these together to give 175760000

Dario Bocchi
Nov 22, 2014

26(4)x10(4)=175760000

0000 number numberplate not valid so....10×10×10×10—1=9999 So 26×26×26×9999=175742424

Heet Bhimani - 6 years, 5 months ago

$26 ( 4 ) \times 10 ( 4 ) = 104 \times 40 = 4160$

. . - 3 months, 3 weeks ago

License Plates

The answer is 175760000.

3 solutions

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