In the Lotsa Millions Lottery, players pick 88 numbers from between 11 and 4242. The order of the numbers doesn't matter and numbers cannot be repeated. To win the jackpot, a ticket must match all 88 numbers. What is the probability that a randomly selected ticket will win the jackpot?
To find the probability that a randomly selected ticket will win the jackpot in the Lotsa Millions Lottery, we need to determine the number of possible winning combinations and divide it by the total number of possible ticket combinations.
There are 88 numbers to choose from, ranging from 11 to 4242. Since the order of the numbers doesn't matter and numbers cannot be repeated, we are dealing with a combination problem.
The total number of combinations can be calculated using the formula for combinations: C(n, r) = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices.
In this case, n = 4232 (4242 - 11 + 1) and r = 88. Thus, the total number of ticket combinations is given by:
C(4232, 88) = 4232! / (88!(4232-88)!)
Next, we need to determine the number of winning combinations. Since all 88 numbers need to be matched, there is only 1 possible winning combination.
Therefore, the probability of winning the jackpot is:
P(winning) = Number of winning combinations / Total number of combinations
= 1 / C(4232, 88)
To calculate this probability, you will need to use a calculator or a computer program that can handle large factorials.
To find the probability of winning the jackpot, we need to determine the number of possible tickets and the number of winning tickets.
The number of possible tickets can be calculated using the concept of combinations. Since players pick 88 numbers out of a range of 11 to 4242, the total number of possible combinations can be calculated using the formula:
nCr = n! / (r!(n-r)!)
Where n is the total number of choices and r is the number of choices we are making.
In this case, n = 4242 - 11 + 1 = 4232, and r = 88. So, the total number of possible tickets is given by:
nCr = 4232! / (88! * (4232-88)!)
Next, we need to determine the number of winning tickets, which is simply 1, since there is only one combination that matches all 88 numbers.
Finally, we can calculate the probability of winning the jackpot by dividing the number of winning tickets by the number of possible tickets:
Probability = Number of winning tickets / Number of possible tickets
= 1 / (4232! / (88! * (4232-88)!))
This gives us the probability that a randomly selected ticket will win the jackpot.