6. The letters A, B, C, and D are to be used in forming four-letter code words. Repetition of letters is not allowed. How many distinct code words can be formed?
Answer: C
24 distinct code words can be formed.
To determine the number of distinct four-letter code words that can be formed using the letters A, B, C, and D without repetition, we calculate the permutations of these 4 letters taken 4 at a time. Thus, the total number of arrangements is 4! = 24.
A) 12
This option is incorrect because it underestimates the total number of permutations. The calculation for distinct arrangements requires considering all available letters, leading to 4! or 24, rather than 12.
B) 16
This option is also incorrect as it does not accurately reflect the total permutations of the letters. The correct calculation involves permutations of 4 letters, which results in 24, not 16.
C) 24
This option is correct. By calculating the permutations of 4 letters taken 4 at a time, we arrive at 4! = 24 distinct arrangements, which matches the requirement of using all letters exactly once.
D) 256
This option is incorrect. It suggests a calculation that may involve repetition or a different interpretation of the problem, but since repetition is not allowed, the correct count remains at 24 distinct combinations.
Conclusion
The correct answer is 24 distinct code words, as derived from the permutations of the four unique letters A, B, C, and D. All other options fail to accurately represent the mathematical principles of permutations without repetition, leading to incorrect totals.