From the digits 1, 2, 3, 4, 5, 6 and 7, how many

Solution

ATQ, Digits available: 1, 2, 3, 4, 5, 6 Even digits (possible last digit): 2, 4, 6 → 3 options We need 4‑digit even numbers, no repetition. Choose the units (last) digit Must be even → 3 choices (2, 4, 6). Fill the thousands, hundreds and tens places After fixing units place, 5 digits remain (all non-zero). Thousands place: any of the remaining 5 digits → 5 ways Hundreds place: any of the remaining 4 digits → 4 ways Tens place: any of the remaining 3 digits → 3 ways Total numbers for each fixed units digit = 5 × 4 × 3 = 60 Total 4‑digit even numbers = (choices for units) × (ways to fill other 3 places) = 3 × 60 = 180