+308 In BINGO, a 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 the bottom right of a BINGO card, in order?
