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 in the first column, 5 numbers from in the second column, 4 numbers in the third column (skipping the WILD square in the middle), 5 numbers from in the fourth column and 5 numbers from in the last column.

One possible BINGO card is:

https://latex.artofproblemsolving.com/1/3/4/134592c325b5c84da1a3e5951091457e0cc2e3fc.png

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 bottom right of a BINGO card, in order?

Guest Apr 10, 2020

#1**+1 **

You don't specify the set(s) from which each separate number can be chosen....

CPhill Apr 10, 2020

#4**0 **

A bingo card contains 5 B-numbers in the range 1, 2, ..., 15;

5 I-numbers in the range 16, 17, ..., 30;

4 N-numbers in the range 31, 32, ..., 45;

5 G-numbers in the range 46, 47, ..., 60;

and 5 O-numbers in the range 61, 62, ..., 75.

The diagonal going from top-left to bottom-right contains one B-number, one I-number, no N-number because of the FREE space, one G-number, and one O-number.

There are 15 x 15 x 15 x 15 possibilities.

geno3141 Apr 10, 2020