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, O's go from 46 through 60, and G's go 61 through 75.
The number of ways N items can be select from M things is:
N for the first one
(N-1) for the second
(N-2) for the third
and so on. Multiplying these all together is the trick!
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.
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 case: We have to divide our number 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 our BINGO calculations, where the 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.
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