Specifically a card is made by placing 5 distinct numbers from the set $1-10$ in the first column, 5 distinct numbers from $11-20$ in the second column, 4 distinct numbers $21-30$ in the third column (skipping the wild square in the middle), 5 distinct numbers from $31-40$ in the fourth column and 5 distinct numbers from $41-50$ in the last column. to play short bingo, someone names numbers, chosen at random, and players mark those numbers on their cards. a player wins when he marks 5 in a row, horizontally, vertically, or diagonally. how many distinct possibilities are there for the values in the first column of a short bingo card? (the placement on the card matters, so the order of the numbers matters, so $5~4~3~2~1$ is to be considered different from $1~2~3~4~5$, for instance.)