A computer code calculates a total of 501 distinct permutations and begins with:
{{2, 2, 2, 2, 2}, {2, 2, 2, 2, 3}, {2, 2, 2, 2, 4}, {2, 2, 2, 2, 7}, {2, 2, 2, 2, 8}, {2, 2, 2, 3, 2}, {2, 2, 2, 3, 4}, {2, 2, 2, 3, 7}, {2, 2, 2, 3, 8}, {2, 2, 2, 4, 2}, {2, 2, 2, 4, 3}, {2, 2, 2, 4, 7}, {2, 2, 2, 4, 8}, {2, 2, 2, 7, 2}, ...........and ends with:
{8, 4, 7, 3, 2}, {8, 7, 2, 2, 2}, {8, 7, 2, 2, 3}, {8, 7, 2, 2, 4}, {8, 7, 2, 3, 2}, {8, 7, 2, 3, 4}, {8, 7, 2, 4, 2}, {8, 7, 2, 4, 3}, {8, 7, 3, 2, 2}, {8, 7, 3, 2, 4}, {8, 7, 3, 4, 2}, {8, 7, 4, 2, 2}, {8, 7, 4, 2, 3}, {8, 7, 4, 3, 2} = 501 permutations.