Chapter 12.6, Problem 55PPE

a.

To determine

To calculate: The number of different call signs that are possible if each station uses a W or K followed by 3 letters.

Answer to Problem 55PPE

There are $35,152$ call signs.

Explanation of Solution

Given information:

The call signs of radio and television stations in the United States generally begin with the letter W east of the Mississippi River and the letter K west of the Mississippi.

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,

The letter W for eats of the Mississippi and the letter K for west of the Mississippi.

The calls signs are formed of 4 alphabets.

So, first place has two choices . That is W or K.

For second place the possibility is 26. As repetition is allowed.

For third place the possibility is again 26 .

For fourth the possibility is again 26.

Therefore,

  $\begin{array}{l}=2\times 26\times 26\times 26\\ =35,152\end{array}$

Hence, there are $35,152$ possible call signs.

b.

To determine

To calculate: The number of different call signs that are possible if each station uses a W or K followed by 4 letters.

Answer to Problem 55PPE

There are $9,13,952$ call signs.

Explanation of Solution

Given information:

The call signs of radio and television stations in the United States generally begin with the letter W east of the Mississippi River and the letter K west of the Mississippi.

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,

The letter W for eats of the Mississippi and the letter K for west of the Mississippi.

The calls signs are formed of 5 alphabets.

So, first place has two choices . That is W or K.

For second place the possibility is 26. As repetition is allowed.

For third place the possibility is again 26 .

For fourth the possibility is again 26.

For fifth the possibility is again 26.

Therefore,

  $\begin{array}{l}=2\times 26\times 26\times 26\times 26\\ =9,13,952\end{array}$

Hence, there are $9,13,952$ possible call signs.