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?

Rationale

24 distinct code words can be formed using the letters A, B, C, and D without repetition.

To determine the number of distinct four-letter code words that can be formed from the letters A, B, C, and D without repeating any letters, we can apply the permutation formula for selecting and arranging items. Since we have four unique letters and we need to arrange all four, the calculation is 4! (4 factorial), which equals 24.

A (12) YOUR ANSWER

This option incorrectly suggests that only 12 code words can be formed. The number of arrangements is calculated using permutations, specifically 4! = 24. Therefore, this choice does not account for all possible arrangements of four letters.

B (16) YOUR ANSWER

Choosing 16 as the number of code words is also incorrect. This number does not reflect the full permutation of the four letters. The correct calculation, as stated, is 4! = 24, which shows that 16 is significantly lower than the actual number of unique arrangements.

C (24) CORRECT

This option accurately represents the total number of distinct code words that can be formed. By calculating the permutations of four different letters (4!), we find that there are indeed 24 possible arrangements, confirming this choice as correct.

D (256) YOUR ANSWER

This choice vastly overestimates the number of distinct code words. The figure 256 could arise from considering repetitions or combinations rather than permutations without repetition. Since repetition is not allowed, the correct calculation remains 4! = 24.

Conclusion

The determination of distinct four-letter code words from the letters A, B, C, and D without repetition results in a total of 24 unique arrangements. Each of the incorrect options fails to grasp the permutation concept required here, emphasizing the importance of accurate calculations in combinatorial problems.

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?

24 distinct code words can be formed using the letters A, B, C, and D without repetition.

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