Question

A BINGO card is a 5 × 5 grid. The center square is a free space and has no number. The first column is filled with five distinct numbers from 1 to 15, the second with five numbers from 16 to 30, the middle column with four numbers from 31 to 45, the fourth with five numbers from 46 to 60, and the fifth with five numbers from61 to 75.
Since the object of the game is to get five in a row horizontally, vertically, or diagonally, the order is important.

How many BINGO cards are there?

Answer 1

Answer:

$5.52*10^{26}$

Step-by-step explanation:

For the columns with 5 slots, there are 15 distinct options to fill in. The number of ways to fill them in is

15 * 14 * 13 * 12 * 11 = 360360 ways (order matters)

For the column with 4 slots and 15 options. The number of ways to fill them in is

15 * 14 * 13 * 12 = 32760  ways (order matters)

Since a bingo card has 4 columns of 5 slots and 1 column with 4 slots, the total number of combination there is:

$360360^4*32760 \approx 5.52*10^{26}$ (order matters)