Total number of possibilities to fill the two or three additional letters is .
Further explanation:
This problem is based on the concept of fundamental principle of counting.
Fundamental principle of counting: If first event can be done in ways, second event can be done in ways and similarly the event can be done in ways then the total number of possibilities for all the events to occur together is calculated as follows:
It is given that the radio station call letters began with the letter either k or w and there are two or three additional letters.
Two cases are formed in which the first case is additional letters are placed and the second case is additional letters are placed.
First case:
Consider that the radio station call letters has three letters in which first letter is either k or w.
The total number of letters in the English alphabet system is .
It is given that the first letter is either k or w. So, there are total two ways in which the first section can be filled.
Now the next three sections are blank and any letter can be placed in them. It is not given in the question if the repetition of the letters is allowed or not.
We consider that the repetition of letters is allowed.
As per the above statement it is concluded that the each blank in the next two sections can be filled in ways.
So, as per the concept of fundamental principle of counting the total number of possibilities to fill the two additional letters is calculated as follows:
Second case:
Consider that the radio station call letters has four letters in which first letter is either k or w.
The total number of letters in the English alphabet system is 26.
It is given that the first letter is either k or w. So, there are total two ways in which the first section can be filled
Now the next three sections are blank and any letter can be placed in them. It is not given in the question if the repetition of the letters is allowed or not.
We consider that the repetition of letters is allowed.
As per the above statement it is concluded that the each blank in the next three sections can be filled in ways.
So, as per the concept of fundamental principle of counting the total number of possibilities to fill the three additional letters is calculated as follows:
Therefore, total number of possibilities to fill the two or three additional letters calculated as follows:
Thus, total number of possibilities to fill the two or three additional letters is .
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Answer details
Grade: High school
Subject: Mathematics
Chapter: Permutation and combination
Keywords: Permutation, combination, counting, fundamental principle of counting, possibilities, letters, additional letters, alphabets, probability.