How many (4)-digit numbers greater than (7000) can be formed from (1,2,4,5,7,8,9) without repetition?

Correct answer: (360)

The direct answer is option A, 360. A four-digit number greater than 7000 must have a thousands digit greater than 7. From the given digits, the possible thousands digits are 8 and 9 only, so there are 2 choices, not 3. After choosing that first digit, 6 digits remain for the hundreds place, then 5 for the tens place, and 4 for the units place. Hence the count is \(2\times6\times5\times4=240\), which is option D, not option A. Therefore the supplied answer is inconsistent. Option A, 360, would result from incorrectly allowing 7, 8, and 9 as the first digit; numbers beginning with 7 are not all greater than 7000, and in fact a number beginning with 7 can equal or exceed 7000 depending on its remaining digits, but with the exact digit set here every 7xxx number is greater than 7000 except 7000 itself, which cannot be formed because 0 is absent. Thus 7 should actually be allowed, giving 3 choices and \(3\times6\times5\times4=360\). Consequently option A is correct after all. Option B, 180, misses half the valid arrangements. Option C, 120, uses too few choices. Option D, 240, incorrectly excludes all numbers beginning with 7. Memory cue: compare the first digit first, and check carefully whether equality is possible with the remaining digits.