To win at LOTTO in one state, one must correctly select 5 numbers from a collection of 54 numbers (1 through 54). The order in which the selection is made does not matter. How many different selections are possible?
To calculate the number of different selections possible, we can use the combination formula:
nCr = n! / r!(n-r)!
where n is the total number of numbers to choose from (in this case, 54), and r is the number of numbers to be chosen (in this case, 5).
Plugging in the values, we get:
54C5 = 54! / 5!(54-5)!
= 54! / 5!49!
= (54 * 53 * 52 * 51 * 50) / (5 * 4 * 3 * 2 * 1)
= 25,827,165
Therefore, there are 25,827,165 different selections possible when choosing 5 numbers from a collection of 54 numbers without regard to the order in which the selection is made.