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# In SHORT BINGO, a $5\times5$ card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares.

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In SHORT BINGO, a  card is filled by marking the middle square as WILD and placing 24 other numbers in the remaining 24 squares.

Specifically a card is made by placing 5 distinct numbers from the set  in the first column, 5 distinct numbers from 1-10 in the second column, 4 distinct numbers 11-20 in the third column (skipping the WILD square in the middle), 5 distinct numbers from 31-40 in the fourth column and 5 distinct numbers from 41-50 in the last column.

One possible SHORT BINGO card is:

To play SHORT BINGO, someone names numbers, chosen at random, and players mark those numbers on their cards. A player wins when he marks 5 in a row, horizontally, vertically, or diagonally.

How many distinct possibilities are there for the values in the first column of a SHORT BINGO card? (The placement on the card matters, so the order of the numbers matters, so 5,4,3,2,1 is to be considered different from 1,2,3,4,5, for instance.)

Dec 9, 2017

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In the first column we can choose any 5 of 10  values and we can arrange these in 5!  ways

So....the total possibilities for the first column =

C(10, 5) * 5!  =    30240

Dec 9, 2017
edited by CPhill  Dec 9, 2017
edited by CPhill  Dec 9, 2017