Chapter 2, Problem 1ST

To determine

The number of ways the call sign of a radio station be formed.

Answer to Problem 1ST

The number of ways the call sign of a radio station be formed based on the given condition is $2\left({26}^3+{26}^2\right)$

Explanation of Solution

The call sign for the ratio station in the United States is a list of three or four letters with first letters from W & K and no restrictions on the other letters is to be estimated.

The total number of alphabets in English language is twenty-six.

The total possibilities for a three letter word shall be $2x26x26$ as the first letter has the possibility only from two letters W & K and the next two letters can be any of the letters where repetition is allowed.

The total possibilities for a four letter word shall be $2x26x26x4$ as the first letter has the possibility only from two letters W & K and the next three letters can be any of the letters where repetition is allowed.

The total number of possibilities shall be the addition of possibilities of three letter word and four letter words. Therefore,

Total number of Possibilities = $2\times 26\times 26+2\times 26\times 26\times 26$

  $=2\times {26}^2\left(26+1\right)$