a We are told that from the east of the Mississippi River the call signs of radio and television generally begin with the letter W. It begins with the letter K from the west of the Mississippi River. If repetition is allowed, we are asked to find the different possible call signs if each station uses a W or K, followed by 3 letters.
East&&Weast
K X X X_(3 letters)&&W X X X_(3 letters)
For both cases, after the first letter we have 26 options to select for the second letter, 26 for the third one, and 26 for the fourth one. Therefore, by the Multiplication Counting Principle we have to multiply 26 by itself three times to find the possible amount of call signs for each case.
26* 26* 26= 17 576
There are 17 576 possible call signs for each side of the Mississippi River. Finally, we need to multiply this value by 2 to get the total number of possible call signs.
17 576* 2=31 152
Therefore, there are 31 152 different possible call signs if each station uses a W or K followed by 3 letters.
b In the same way, we can calculate the possible call signs if the station uses W or K followed by 4 letters. In this case, we first have to multiply 26 by itself four times.
26* 26* 26* 26= 456 976
Finally, let's multiply this value by 2 to get the total number of possible call signs.
456 976* 2=913 952
Therefore, there are 913 952 different possible call signs if each station uses a W or K followed by 4 letters.
