Using the digits (1,2,3,4,5,6,7) without repetition (2)-digit numbers are formed. The number must be greater than (50). How many numbers are possible?

Correct answer: (18) numbers

The direct answer is A: 18 numbers. To be greater than 50, the tens digit must be 5, 6, or 7. Thus there are 3 choices for the tens place. After choosing it, one digit has been used, so 6 of the remaining digits can be placed in the units position. Repetition is forbidden, so the total is \(3\times6=18\). Option A is correct. Option B, 21, would incorrectly allow 7 choices for the units digit for every tens digit, including reuse of the tens digit. Option C, 14, does not count all valid units choices. Option D, 28, is the total number of ordered two-digit selections without applying the greater-than-50 restriction. Notice that 50 itself cannot be formed because digit 0 is unavailable, and all numbers beginning with 5, 6, or 7 are greater than 50. Memory cue: choose the restricted first digit first, then count the remaining digits.