n BINGO, a $5\times5$ card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares. Specifically a card is made by placing 5 numbers from the set $1-15$ in the first column, 5 numbers from $16-30$ in the second column, 4 numbers $31-45$ in the third column (skipping the WILD square in the middle), 5 numbers from $46-60$ in the fourth column and 5 numbers from $61-75$ in the last column. One possible BINGO card is: To play 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 diagonal going from top left to bottom right of a BINGO card, in order