Question

In a certain state's lottery, 45 balls numbered 1 through 45 are placed in a machine and eight of them are drawn at random. If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000. In this lottery, the order the numbers are drawn in does not matter. Compute the probability that you win the million-dollar prize if you purchase a single lottery ticket.

Answer 1

The required probability is
`(1)/(215553195)\approx0.000000004639`

Explanation:

Consider the provided information.

If the eight numbers drawn match the numbers that a player had chosen, the player wins $1,000,000.

Determine the total number of ways 8 numbers can be drawn,

Since the order the numbers are drawn in does not matter the number of possible outcomes of the lottery drawing is :
`^(45)C_8 = (45!)/(8!37!)=215553195`

Only one would match all 8 numbers on the player’s ticket,

Therefore, the probability of winning the grand prize is:

`(^8C_8)/(^(45)C_8)=(1)/(215553195)\approx0.000000004639`

Hence, the required probability is
`(1)/(215553195)\approx0.000000004639`