Final answer:
To determine how many strings of four hexadecimal digits have no repeated digits, use permutations of 16 choices for the first digit, 15 for the second, 14 for the third, and 13 for the fourth. The calculation results in 43,680 such strings, which is answer B.
Step-by-step explanation:
The question is asking about possible combinations of four-digit hexadecimal numbers without any digit repeating. Hexadecimal digits include 0-9 and A-F, giving us 16 possible choices for each digit. However, since we cannot have any digits repeated, we must use permutations to find the number of combinations where order matters and no digit repeats.
The first digit can be any of the 16 hexadecimal digits. Once the first digit is chosen, we have 15 options left for the second digit, as it cannot be the same as the first. For the third digit, 14 options remain, and for the fourth digit, 13 options are left. Therefore, the total number of non-repeating four-digit hexadecimal strings is calculated by multiplying these numbers together (16 × 15 × 14 × 13).
Calculating this gives us 16 × 15 × 14 × 13 = 43,680.
So, the correct answer is B. 43,680 strings of four hexadecimal digits do not have any repeated digits.