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If you win the lottery by selecting six out of 50 numbers from 0 to 49 in any order, what is the probability of winning the lottery?

a) 1/1225
b) 1/19600
c) 1/2118760
d) 1/13983816

1 Answer

3 votes

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.

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