In SHORT 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 distinct numbers from the set in the first column, 5 distinct numbers from 1-10 in the second column, 4 distinct numbers 11-20 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.
One possible SHORT BINGO card is:
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.)