Chapter 8.3, Problem 75E

Bingo Bingo has become popular in the United States, and it is an efficient way for many organizations to raise money. The bingo card has 5 rows and 5 columns of numbers from 1 to 75, with the center given as a free cell. Balls showing one of the 75 numbers are picked at random from a container. If the drawn number appears on a player's card, then the player covers the number In general, the winner is the person who first has a card with an entire row, column, or diagonal covered. Source: Mathematics Teacher.

(a) Find the probability that a person will win bingo after just four numbers are called.

(b) An L occurs when the first column and the bottom row are both covered. Find the probability that an L will occur in the fewest number of calls.

(c) An X-out occurs when both diagonals are covered. Find the probability that an X-out occurs in the fewest number of calls.

(d) If bingo cards are constructed so that column one has 5 of the numbers from 1 to 15, column two has 5 of the numbers from 16 to 30, column three has 4 of the numbers from 31 to 45, column four has 5 of the numbers from 46 to 60, and column five has 5 of the numbers from 61 to 75, how many different bingo curds could be constructed? (Hint: Order matters!)