Each of the digits 6,7,8,9 is used no more than once to form an integer N. How many possible Ns are multiples of $4$?
{{6, 7, 8, 9}, {6, 7, 9, 8}, {6, 8, 7, 9}, {6, 8, 9, 7}, {6, 9, 7, 8}, {6, 9, 8, 7}, {7, 6, 8, 9}, {7, 6, 9, 8}, {7, 8, 6, 9}, {7, 8, 9, 6}, {7, 9, 6, 8}, {7, 9, 8, 6}, {8, 6, 7, 9}, {8, 6, 9, 7}, {8, 7, 6, 9}, {8, 7, 9, 6}, {8, 9, 6, 7}, {8, 9, 7, 6}, {9, 6, 7, 8}, {9, 6, 8, 7}, {9, 7, 6, 8}, {9, 7, 8, 6}, {9, 8, 6, 7}, {9, 8, 7, 6}}==24 permutations
Only: 7896, 7968, 8796, 8976, 9768, 9776==6 are divisible by 4, or are multiples of 4.
