In SHORT BINGO, a 5 x 5 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 - 10 in the first column, 5 numbers from 11 - 20 in the second column, 4 numbers 21 - 30 in the third column (skipping the WILD square in the middle), 5 numbers from 31 - 40 in the fourth column and 5 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 row of a SHORT BINGO card?