# college

posted by .

if a license plate consists of 2 letters followed by 4 digits, how many different plates could be created having at least one letter or digit repeated?

I know its not 6,760,000

• college -

consider the Pr of two letters the same: 1/26

Now consider the Pr of two numbers: 1/10*9/10*8/10
Now the Pr of three numbers the same:
1/10*1/10*9/10
now the Pr of four numbers the same:
1/10*1/10*1/10
now the pr of having two pairs of numbers the same:
1/10*9/10*1/9

Pr(at least one letter or digit repeated:
sum of (two letters, no numbers) + (two letters, two numbers)+(two letters, three numbers)+(two letters, four numbers)+(two letters, two pairs of numbers) + (no letters, two numbers)+(no letters, threenumbers)+(no letters, four numbers)+ (no letters,two pairs of numbers)

I will do the first four probabilities for you:
Pr(twoletters, no numbers)=1/26*9/10*8/10*7/10
Pr(two letters, two numbers)=1/26*1/10*9/10*8/10
Pr(two letters, three numbers)=1/26*1/10*1/10*9/10
See if you can finish.

• college -

,ll

• college -

First find the number of combinations if all letters and numbers can be repeated
(26*26*10*10*10*10)=6760000

Then find the number of combinations if none were repeated
(26*25*10*9*8*7)=3276000

(value of combinations that can be repeated)-(value of combinations that no letter or number could be repeated) = 6760000-3276000= 3484000

## Similar Questions

1. ### Statistics

Find the possible nuber of license plates consisting of 2 letters followed by 4 digits if digits can be repeated but letters can not a. 3,276,000 b. 3,407,040 c. 6,500,000 d. 6,760,000 I thought 26*24*24*23*22*21*20 etc/9 but that …
2. ### algebra

In Utah, a license plate consists of 3 digits followed by 3 letters. The letters I, O, and Q are not used, and each digit or letter may be used more than once. How many different license plates are possible?
3. ### math please check my work

a license plate has 2 letters followed by 4 digits.how many license plates are possible if the digits and letters can be repeated?
4. ### algebra

If license numbers consist of 3 letters followed by 3 digits, how many different licenses could be created having at least one letter or digit repeated?
5. ### Computers

In Python - A state creates license plates, each containing two letters followed by three digits. The first letter must be a vowel (A,E,I,O,U), and duplicate letters and digits are allowed. The second letter can be any letter of the …
6. ### Math

What is the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have one numeral followed by three letters followed by three numerals?
7. ### College probability and statistics

The current license plates in New York State consist of three letters followed by four digits. ( i ) How many possible distinct license plates can there be?
8. ### Algebra

What is the probability of getting a license plate that has a repeated letter or digit if you live in a state in which license plates have one numeral followed by three letters followed by three numerals?
9. ### Pre

How many different license plate number can be made using 2 letters followed by 4 digits selected from the digits 0-9 a) if letters and digits may be repeated?
10. ### Math

A license plate consists of 3 letters followed by 2 digits. How many license plates are possible if the 1st letter cannot be I nor O, the 1st digit cannot be 0, and no letters or digits may repeat?

More Similar Questions