Chapter 12.6, Problem 48PPE

a.

To determine

To calculate: The number of different license plates possible in each country.

Answer to Problem 48PPE

There are $2,60,000$ licenses plates per country.

Explanation of Solution

Given information:

In one state , a regular license plate has a two-digit number that is fixed by country, then one letter, and then four one-digit numbers.

Formula used:

For any positive integer $n$, the expression $n$ factorial is written as $n!$ and is the product of integers from n down to 1.

Calculation:

According to the question,

Since license number is formed by using numbers and alphabets. It consist of 7 −digit license plate.

So, first two digits are fixed by the country. Now there are 5 digits to occupy.

For third place the possibility is 26. As after two digits , one alphabet is to be placed.

For fourth place the possibility is 10 . As numbers are placed from 0 to 9.

For fifth place the possibility is 10. As numbers are placed from 0 to 9.

For sixth the possibility is 10. As numbers are placed from 0 to 9.

For seventh the possibility is 10. As numbers are placed from 0 to 9.

Therefore,

  $\begin{array}{l}=26\times 10\times 10\times 10\times 10\\ =2,60,000\end{array}$

Hence, there are $2,60,000$ possible license plates per country.

b.

To determine

To calculate: the number of license plates possible in the entire state.

Answer to Problem 48PPE

There are $2,39,20,000$ license plates in entire country.

Explanation of Solution

Given information:

There are 92 countries in the state.

Formula used:

To find the number of items on the given of cost , price of only one item , multiply the two numbers.

Calculation:

According to the question,

There are $2,60,000$ possible license plates per country.

Total number of countries are 92.

  $\begin{array}{l}=2,60,000\times 92\\ =2,39,20,000\end{array}$

Hence, there are $2,39,20,000$ possible license plates in the entire country.