What is the most number of bingo cards that can be made without repeating any cards?

The numbers in each column are limited also: B has 1-15; I has 16-30; N has 31-45; G has 46-60; O has 47 -75.

Assuming you care about the order of the numbers, you need to use permutations. For most columns, you will use 5 numbers from the set of 15, so the number of possible arrangements in each column is:

15!/(10!) = 360,360

For the N column you only use 4 numbers, so there are only 32,760 arrangements,

If you take 360,360 and raise it to the fourth power, then multiply by 32,760 you'll get the full answer. It's on the order of 10^25.

If you don't care about the order, you'll use combinations. The formula would be:

15! / (10! * 5!) = 3,003 and

15! / (11! * 4!) = 1365

It's on the order of 10^16.