Radio stations use three or four letters for their call letters(name). The first letter must be a W or K. How many different call letters are possible if repeated letters are allowed? And not allowed?
3-letter permutations:
= 2x26x26 = 1352
4-letter permutations:
= 2x26x26x26 = 35152
total = 36504
If not repetition allowed
3-calls = 2x25x24 =
4 letters = 2x25x24x23 =
total = ..
Fille in the blank
1,3,5,7,9,11,13,15
If repeated letters are allowed, there are 26 choices for each of the three or four letters in the call letters. Therefore, the number of different call letters possible is:
For three-letter call letters: 26 * 26 * 26 = 17,576
For four-letter call letters: 26 * 26 * 26 * 26 = 456,976
If repeated letters are not allowed, then the first letter can be W or K, and the subsequent letters can be any letter except the one that has already been chosen. Therefore, the number of different call letters possible is:
For three-letter call letters: 2 * 25 * 24 * 23 = 27,600
For four-letter call letters: 2 * 25 * 24 * 23 * 22 = 303,600
To determine the number of different call letters possible for radio stations, we need to consider two scenarios: when repeated letters are allowed and when they are not allowed.
Scenario 1: Repeated letters are allowed.
In this case, we can have any letter from A to Z in each of the three or four positions, including the letters W and K as the first letter. Since there are 26 letters in the English alphabet, the number of possible call letters with repeated letters allowed is:
For a three-letter call sign: 26 x 26 x 26 = 17,576 possible combinations.
For a four-letter call sign: 26 x 26 x 26 x 26 = 456,976 possible combinations.
Scenario 2: Repeated letters are not allowed.
In this case, we need to consider that the first letter must be either W or K, and for the remaining positions, we can have any of the remaining 25 letters from A to Z. The number of possible call letters with repeated letters not allowed is:
For a three-letter call sign: 2 x 25 x 25 = 1,250 possible combinations.
For a four-letter call sign: 2 x 25 x 25 x 25 = 31,250 possible combinations.
So, the total number of different call letters with repeated letters allowed and not allowed are as follows:
With repeated letters allowed:
- Three-letter call sign: 17,576 possible combinations.
- Four-letter call sign: 456,976 possible combinations.
With repeated letters not allowed:
- Three-letter call sign: 1,250 possible combinations.
- Four-letter call sign: 31,250 possible combinations.