Final answer:
The probability of winning the lottery by selecting six out of 50 numbers from 0 to 49 in any order is 1/15,890,700.
Step-by-step explanation:
To calculate the probability of winning the lottery by selecting six out of 50 numbers from 0 to 49 in any order, we need to use the formula for the number of combinations. The formula is:
C(n, k) = n! / (k! * (n - k)!)
Where n is the total number of numbers to choose from (in this case, 50) and k is the total number of numbers to be chosen (in this case, 6). Using this formula:
C(50, 6) = 50! / (6! * (50 - 6)!)
Simplifying the equation:
C(50, 6) = 50! / (6! * 44!)
Calculating the factorial:
50! = 50 * 49 * 48 * 47 * 46 * 45 * 44!
6! = 6 * 5 * 4 * 3 * 2 * 1
44! = 44 * 43 * 42 * 41 * 40 * ... * 1
Plugging the values into the formula:
C(50, 6) = (50 * 49 * 48 * 47 * 46 * 45 * 44!) / ((6 * 5 * 4 * 3 * 2 * 1) * 44!)
Canceling out the common terms in the numerator and denominator:
C(50, 6) = (50 * 49 * 48 * 47 * 46 * 45) / (6 * 5 * 4 * 3 * 2 * 1)
Simplifying the equation:
C(50, 6) = 15,890,700
The total number of possible outcomes (microstates) is 15,890,700. Therefore, the probability of winning the lottery is 1 out of 15,890,700, which can be written as 1/15,890,700.