HOW MANY FOUR-LETTER CODE WORDS CAN BR FORMED USING A STANDARD 26-LETTER ALPHABET
IF REPETITION IS ALLOWED
IF REPETITION IS NOT ALLOWED
To find the number of four-letter code words that can be formed using a standard 26-letter alphabet, we can use basic combinatorial principles.
If repetition is allowed:
Since repetition is allowed, each of the four positions in the code word can be filled with any of the 26 letters. Therefore, for each position, we have 26 choices. Since the positions are independent of each other, we can multiply the number of choices for each position to find the total number of code words.
So, the number of code words with repetition allowed is: 26^4 = 456,976.
If repetition is not allowed:
If repetition is not allowed, each position in the code word can only be filled with a different letter from the alphabet. For the first position, we have 26 choices, for the second position, we have 25 choices (since we cannot choose the same letter as the first position), for the third position, we have 24 choices, and for the fourth position, we have 23 choices.
Therefore, the number of code words with no repetition is: 26 * 25 * 24 * 23 = 358,800.
In summary:
- If repetition is allowed, there are 456,976 four-letter code words that can be formed.
- If repetition is not allowed, there are 358,800 four-letter code words that can be formed.