# College probability and statistics

posted by Melissa

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?
( ii ) How many possible distinct license plates could there be if the letters O and I and the digits, 0 and 1 were prohibited because they look alike?
( iii ) How many different license plates are there that have precisely two C's and two 2's? (Here we are no longer prohibiting O's, I's, 0's and 1's.) [Hint: Consider placing the two C's in position and then filling in the other letter. Do something similar with the digits

1. Reiny

3 letters ---> 26^3
--- 10^4

number of plates = 26^3 (10^4) = 175760000

(about 176 million, long way to go)

ii) so only 24 letters, and 8 numbers
-- what do you think?

iii) look at the letter part first:
assume we put CC at the front
so number of such cases = 1x1x25x25 = 625
CCMP could be one those, but each one can be arranged in 4!/2! or 12 ways
the letters can be arranged in 625x12 or 7500 ways
using the same argument for the numbers, there are
1x1x9x9 x 12 ways or 972 ways
number of ways according to the stated conditions
= 7500x972 = 7290000 ways

2. Anonymous

8585

## Similar Questions

1. ### Math

A license plate is to consist of two letters followed by three digits. How many different license plates are possible if the first letter must be a vowel, and repetition of letters is not permitted, but repetition of digits is permitted?
2. ### math

A state's license plate contains 3 letters followed by 3 digits. How many different license plates are possible?
3. ### pre calculus

A state makes auto license plates that have two letters (excluding I, 0, and Q) followed by four digits of which the first digit is not zero. How many different license plates are possible?
4. ### college math

a license plate is to consist of three digits followed by two uppercase letters. determine the number of different license plates possible. the first digit cannot be zero and repition is not permitted.
5. ### Math

A state creates license plates that each contain 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. How many different license plates are possible?
6. ### survey of math

A license plate is to consist of 2 letters followed by 3 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted?
7. ### statistics

A license plate is to have 3 digits followed by 2 uppercase letters. What is the number of different license plates possible if repetition of numbers and letters is not permitted?
8. ### Computer Programming

I am trying to put the following in Python Code. I know how to do it mathematically, but code - not sure where to start. A state creates license plates that each contain two letters followed by three digits. The first letter must be …
9. ### 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 …
10. ### Math

How do I work this problem? A license plate is to consist of 2 letters followed by 5 digits. Determine the number of different license plates possible if repetition of letters and numbers is not permitted. is this correct 26*26*10*10*10*10*10=

More Similar Questions