How many (3)-digit numbers greater than (400) can be formed from (1,2,4,6,8) without repetition?

Correct answer: (36)

The direct answer is option A: 36 numbers. A three-digit number greater than 400 must have a hundreds digit greater than 4, because 4 in the hundreds place would give a number beginning with 4, which is not greater than 400 unless the remaining digits make it greater; here the available digits after 4 can indeed make such numbers, so we must check carefully. If the hundreds digit is 4, the tens and units can be selected in \(4\times3=12\) ways, and all are greater than 400 because the remaining two-digit part is positive. If the hundreds digit is 6 or 8, there are also \(4\times3=12\) ways for each. Thus the total is \(3\times12=36\), counting hundreds digits 4, 6, and 8. Option A is correct. Option B, 60, ignores the restriction or overcounts. Option C, 24, misses one allowed hundreds-digit case. Option D, 48, is another overcount. No digit repeats. Exam cue: for “greater than 400,” inspect the hundreds digit and remember that 4xx is greater than 400 when the last two digits are nonzero.