Question

In 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 numbers from the set 1-15 in the first column, 5 numbers from 16-30 in the second column, 4 numbers 31-45 in the third column (skipping the WILD square in the middle), 5 numbers from 46-60 in the fourth column and 5 numbers from 61-75 in the last column.



One possible BINGO card is:


To play 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 diagonal going from top left to the bottom right of a BINGO card, in order?

Answer 1

Answer:

33

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Answer 2

Given:

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

To find:

How many distinct possibilities are there for the values in the diagonal going from top left to the bottom right of a BINGO card, in order?

Solution:

From given, we have,

4 choices

15 options for each choice

The number of possibilities is given by,

N = Options ^Choices

Therefore, we get,

∴ N = 15^4 = 50625

Therefore 50625 distinct possibilities are there for the values in the diagonal going from top left to the bottom right of a BINGO card, in order.