The call letter of a radio station must have 4 letters.The first letter must be a K or a W. How many different station call setters can be made if repetitions are not allowed? If repetitions are allowed?
With no repetition, there are 2 choices for the first letter
25 choices for the second
24 choices for the third
23 choices for the last.
Use the multiplication rule to find the total number of possible names.
Bano ka
To determine the number of different station call letters that can be made, we need to consider two scenarios: when repetitions are not allowed and when repetitions are allowed.
Case 1: Repetitions are not allowed
In this case, we can treat the selection of each letter as an independent event.
The first letter can be either a 'K' or a 'W', so there are two choices for the first letter.
Since repetitions are not allowed, there are 25 choices remaining for the second letter (excluding the letter already chosen for the first position).
Similarly, there are 24 choices for the third letter and 23 choices for the fourth letter.
Using the multiplication principle, the total number of different station call letters that can be made without repetitions is:
2 x 25 x 24 x 23 = 27,600
Therefore, when repetitions are not allowed, there are 27,600 different station call letters that can be made.
Case 2: Repetitions are allowed
In this case, we can still treat each letter selection as an independent event, but now there are no restrictions on repetitions.
The first letter can be either 'K' or 'W', so again there are two choices.
For the second letter, since repetitions are now allowed, there are 26 choices available (all alphabet letters plus the 'K' or 'W' option).
Similarly, there are 26 choices for the third letter and 26 choices for the fourth letter.
Using the multiplication principle, the total number of different station call letters that can be made with repetitions allowed is:
2 x 26 x 26 x 26 = 35,152
Therefore, when repetitions are allowed, there are 35,152 different station call letters that can be made.
To summarize:
- When repetitions are not allowed, there are 27,600 different station call letters that can be made.
- When repetitions are allowed, there are 35,152 different station call letters that can be made.