Chapter 1, Problem 1.1P

a. How many different 7-place license plates are possible if the first 2 places are for letters and the other 5 for numbers?

b. Repeat part (a) under the assumption that no letter or number can be repeated in a single license plate.

To determine

The number of different 7-place license plates.

Answer to Problem 1.1P

67600000

Explanation of Solution

Given:

First 2 places are for letters.

Other 5 places are for numbers.

Calculation:

Total number of letters is 26 (A to Z)

Total number of digits is 10 (0 to 9)

Applying the basic principle of counting, number of license plates will be

  $\begin{array}{l}=26\times 26\times 10\times 10\times 10\times 10\times 10\\ =67600000\end{array}$

To determine

The number of different 7-place license plates.

Answer to Problem 1.1P

19656000

Explanation of Solution

Given:

First 2 places are for letters.

Other 5 places are for numbers.

No letter or number can be repeated in a single license plate.

Calculation:

As there can be no repetition,

The first place letter has 26 options.

The second place letter has 25 options.

The third place digit has 10 options.

The fourth place digit has 9 options.

The fifth place digit has 8 options.

The sixth place digit has 7 options.

The seventh place digit has 6 options.

Applying the basic principle of counting, number of license plates will be

  $\begin{array}{l}=26\times 25\times 10\times 9\times 8\times 7\times 6\\ =19656000\end{array}$