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.)

RektTheNoob
Dec 9, 2017