To win a state "A" lottery, one must correctly select 5 numbers from a collection of 50 numbers (1 through 50). The order in which the selection is made does not matter. The neighboring state "B" has a lottery where one must correctly select 6 numbers from a collection of 60. Which lottery would you rather play? Support your choice with mathematical calculations.

Question

Mathematics

Rowan

5 January, 11:44

To win a state "A" lottery, one must correctly select 5 numbers from a collection of 50 numbers (1 through 50). The order in which the selection is made does not matter. The neighboring state "B" has a lottery where one must correctly select 6 numbers from a collection of 60. Which lottery would you rather play? Support your choice with mathematical calculations.

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Dex · Answer 1

The number of possibilities for the first one is 50 choose 5, and the number of possibilities for the second one is 60 choose 6. Since 50 choose 5 is 2118760 and 60 choose 6 is 50063860. There are less possible outcomes for state "A" and therefore you have a higher chance of winning.