To win at LOTTO in a certain state, one must correctly select 6 numbers from a collection of 52 numbers (1 through 52). The order in which the selections is made does not matter. How many different 6-number selections are possible?

The answer is 20,358,520

Step-by-step explanation:

Selecting 6 numbers from a collection of 52 numbers regardless of order involves a combination.

Note: if regards was taken into order of selection, this would be a permutation.

Hence, the different 6 number selections out of 52 is

52C6 = 52! / [6!*(52-6)!]

= 52!/(6!*46!)

= 20,358,520

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