First, you must determine how many tickets are possible. In your state, the lottery balls have the numbers
1-46 on them and you must pick 6 numbers.
a. Determine how many possible tickets exist for your state lottery.
b. Now, you need to come up with a plan to buy all those tickets. With your group, develop a scheme to do
this. Be sure to include all costs, number of people involved, and any other information crucial to the plan.
You will be asked to explain and justify the method to the rest of the class. You may assume that the entire
jackpot is yours if you win in immediate cash. (Even though this is not true!)
A research company out hears about your operation and wants to know what the lowest jackpot would have
to be to guarantee at least $1 dollars for each person involved in the plan.
c. Determine the lowest jackpot for your plan. Would you revise your plan given this idea?
a. To determine the number of possible tickets for the state lottery, we need to calculate the combination. Since you need to pick 6 numbers out of 1-46, the formula for combination is applied:
C(n, k) = n! / (k!(n-k)!)
In this case, n = 46 (the range of numbers) and k = 6 (the number of numbers to be picked). Plugging in these values, we get:
C(46, 6) = 46! / (6!(46-6)!)
= 46! / (6!40!)
= (46*45*44*43*42*41) / (6*5*4*3*2*1)
= 9,366,819
Therefore, there are 9,366,819 possible tickets for the state lottery.
b. Buying all the possible tickets is not a feasible plan due to various reasons such as the high cost, logistical challenges, and time constraints. However, if we assume that it is possible, let's break down the plan:
1. Cost: Each ticket costs a certain amount. To buy all the tickets, we need to multiply the cost of a single ticket by the total number of tickets (9,366,819). This will give us the total cost of buying all the tickets.
2. Number of people involved: We need to divide the workload among a group of people. Each person can be assigned a certain number of tickets to purchase. The number of people required will depend on factors such as time constraints, availability of resources, and dimensions of the operation. It's essential to consider the efficiency and synchronization of the group to ensure smooth execution.
3. Additional information: Other crucial information includes the timeframe to purchase all the tickets, security measures to protect the tickets, logistics for organizing and managing the large number of tickets, and coordination among the group members.
c. To calculate the lowest jackpot required to guarantee at least $1 for each person involved in the plan, we need to divide the total cost of buying all the tickets (determined in part b) by the number of people involved.
Let's assume there are M people involved in the plan. The lowest jackpot required would be:
Lowest Jackpot = (Total cost of buying all tickets) / M
Once we calculate this value, it would represent the minimum jackpot needed to distribute $1 to each person involved. If the calculated lowest jackpot is higher than the actual jackpot, it means the plan would not guarantee at least $1 for each person.
Considering the impracticality and high costs of buying all tickets, it is recommended to revise the plan and explore other strategies for participating in the lottery.