How Many Possible Bingo Cards Are There

Each column of an 80-ball bingo card contains 4 numbers. These numbers are selected from 20 possibilities: for example, the first column can contain any 4 numbers from 1 to 20 inclusive. On an 80-ball bingo card, the order in which the numbers appear is significant and can vary. For example, a card with the numbers 1, 13, 19, 14 in the first column is different from one with the …

In total, there are 2 different possibilities of laying out the outside of each of the four cubes which are identical from a gameplay perspective. This means that for a set of numbers that could appear on the card, there are 2 x 2 x 2 x 2 = 16 total possibilities in the calculation we made in part 1 which would produce an identical game result.

We are not talking thousands, millions, billions or even trillions of possible cards, there are in fact 552 septillion possible card combinations for 75-ball bingo. If you write that number out it looks like this with 552 followed by a further 24 digits: 552,446,474,061,128,648,601,600,000 or 552 Septillion possible unique 75-ball bingo cards.

Each column of a 50-ball bingo card contains 2 numbers. These numbers are selected from 10 possibilities: for example, the first column can contain any 2 numbers from 1 to 10 inclusive. On a 50-ball bingo card, the order in which the numbers appear is significant and can vary. For example, a card with the numbers 15 at the top of the second column and 17 below it is …

24,069,639,359,475,000 or 24 Quadrillion possible unique 90-ball bingo cards. Printing cards at 1 per second would mean we could print 31,536,600 cards per year (taking leap years into account), yet it would still take 763,228,736 years of constant printing to produce all the possible 90-ball bingo card combinations. That is 15% of the time the planet earth has existed so far …