Winning the LotteryResponse • 30 pointshttps://www.flalottery.com/exptkt/lottoodds.pdfIn the above scenario, when there were 53 numbers to choose from, and players pick 6 numbers, the total number of combinations was 22,957,480. The calculations for this are shown step by step in the above image using the Combination formula. Use the information above to answer the following questions: 1. What are the odds of winning in this scenario with one winning ticket? 2. What would the odds of winning be if there are 54 numbers instead of 53 with one winning ticket?3. Suppose the Lottery Commission offers a Pick 5 game, where the players choose 5 out of 40 numbers. What would the odds of winning be if there are three winning tickets in this drawing?
Question
Winning the LotteryResponse • 30 pointshttps://www.flalottery.com/exptkt/lottoodds.pdfIn the above scenario, when there were 53 numbers to choose from, and players pick 6 numbers, the total number of combinations was 22,957,480. The calculations for this are shown step by step in the above image using the Combination formula. Use the information above to answer the following questions: 1. What are the odds of winning in this scenario with one winning ticket? 2. What would the odds of winning be if there are 54 numbers instead of 53 with one winning ticket?3. Suppose the Lottery Commission offers a Pick 5 game, where the players choose 5 out of 40 numbers. What would the odds of winning be if there are three winning tickets in this drawing?
Solution
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The odds of winning in this scenario with one winning ticket is 1 in 22,957,480. This is because there is only one winning combination out of a total of 22,957,480 possible combinations.
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If there are 54 numbers instead of 53, we would need to calculate the total number of combinations for picking 6 numbers out of 54. This can be calculated using the combination formula C(n, r) = n! / [r!(n-r)!], where n is the total number of items, and r is the number of items to choose. Plugging in the values, we get C(54, 6) = 54! / [6!(54-6)!] = 25,827,165. So, the odds of winning with one ticket would be 1 in 25,827,165.
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For the Pick 5 game, where players choose 5 out of 40 numbers, we would calculate the total number of combinations as C(40, 5) = 40! / [5!(40-5)!] = 658,008. If there are three winning tickets, the odds of winning would be 3 in 658,008, or simplified, 1 in 219,336.
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