Question

The Mega Millions lottery is available in multiple states including New Jersey. A Mega Millions ticket consists of 5 different numbers from 1 to 70, followed by the "Mega Ball" number which is a number 1 to 25. To win the jackpot the player must match all 6 numbers (the 5 chosen from 1 to 70, and the Mega Ball number). The order of the numbers does not matter. If you were to purchase a single ticket, what is the probability that you'll win the jackpot?
A. 1/302575350

B. 1/42017500000

C. 1/36309042000

D. 1/12103014

Answer 1

Using the combinations formula, the probability that you'll win the jackpot is given by:

A. 1/302575350.

What is the combination formula?

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by:

$C_{n,x} = \frac{n!}{x!(n-x)!}$

5 numbers are selected from a set of 70, along with one number from a set of 25, hence the number of combinations is given by:

$C_{70,5}C_{25,1} = \frac{70!}{5!65!} \times \frac{25!}{1!24!} = 302575350$

Only one combination is correct, hence the probability of winning is given by:

A. 1/302575350.

More can be learned about the combination formula at brainly.com/question/25821700

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