There are 5 Columns on a Bingo Card, each labeled with the letters from
** BINGO**. Under each letter can be 5 of 15 possible numbers, and no
number appears more than once on any Bingo Card. **B**'s go from 1
through 15, **I**'s go from 16 through 30, **N**'s go from 31
through 45, **G**'s go from 46 through 60, and **O**'s go 61
through 75.

The number of ways X items can be select from M things is:

X for the first one

(X-1) for the second

(X-2) for the third

and so on. Multiplying these all together is **the number of ways!**

A simple example would be: **How many two letter "words", with no
repeating letters, can be formed from the letters "ABCDE"?** The first
could be any one of the 5 letters and the second could be any of the
remaining 4. So the number of ways would be 5 times 4 or 20. This would
also be the number of ways a President and Vice-President could be
selected from a group of five people.

*There would be 60 possible three letter words.*

A word of warning here: *In the above examples ***order counts**.
"**BD**" is a different word than "**DB**", the same for President
& Vice President. If we were just selecting a committee of two from
five people it would not mater what order they were "drawn" it would
result in the same committee. For this: We have to divide by the number
of ways two could be selected from the two drawn. For this example it
would be 2 times 1 or two. **Only 10 committees could be selected from 5
people.**

## Back to 75 Ball BINGO Card calculations

**Order drawn does
count**. For the "B" column we are selecting 5 things from 15, and if
we ignore the "Free" cell in the center it is the same for each of the 5
columns.

### 15*14*13*12*11 = 360,360

If we multiply __360,360__ by itself five times we get:

### 6,076,911,214,672,415,134,617,600,000

This would be the number of different BINGO cards if all the columns
were the same. __No "Free" space under the "N"__ But if we only allow four
values for the N Column, the 11 should not have been multiplied in for
the N column. We can take it out by dividing the above number by 11.
Giving us:

### 552,446,474,061,128,648,601,600,000

Possible BINGO cards!

*This agrees with the number calculated on a WiKi page.*

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