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 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 31-40in the fourth column and 5 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 row of a SHORT BINGO card?

Echotastic Feb 17, 2018