A group of us were playing Bingo. I noticed
something very interesting. There were different Bingo cards with no two cards
having the same set of numbers in corresponding column or row. The centre of
course was a free space.
How many such cards are possible, can you
tell?
Answer: The N column is the most
restrictive column since it has only four open choices, instead of the five
usual choices. These four choices must be made from the set (31, 32, 33……….43,
44, 45) which contain fifteen elements. Thus when we have made all possible
selections of 4 numbers from 15 numbers, we will have reached the total
possible number of different Bingo cards.
(15 /4) = 15 × 14× 13× 12 / 4 ×3× 2 ×
1 = 1365
888 + 88+ 8 + 8 +8 =1000
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