The probability of winning with the very first Lotto ticket you purchase of the Lotto game consisting of picking 6 of 48 numbers is 1/12271512 or approximately 0.0000000815.
A permutation is a process of calculating the number of ways to choose a set from a larger set in a particular order.
If we want to choose a set of r items from a set of n items in a particular order, we find the permutation nPr = n!/(n-r)!.
A combination is a process of calculating the number of ways to choose a set from a larger set in no particular order.
If we want to choose a set of r items from a set of n items in no particular order, we find the combination nCr = n!/{(r!)(n-r)!}.
In the question, we are asked to determine the probability of winning a lottery by picking 6 numbers from 48 numbers with the first ticket we purchase.
First, we need to calculate the number of combinations of choosing 6 numbers from 48 numbers. As we need to consider no particular order, we will use combinations,
48C6 = 48!/{(6!)(48-6)!} = 48!/(6!*42!) = (43*44*45*46*47*48)/(1*2*3*4*5*6*) (As 48! = 42!*43*44*45*46*47*48, and 42! cancels itself from the numerator and the denominator).
or, 48C6 = 12,271,512.
So, we get the number of combinations = 12,271,512.
We know that we will choose only one particular set of 6 numbers.
∴ The probability of winning on the very first ticket = 1/12,271,512 ≈ 0.0000000815
∴ The probability of winning with the very first Lotto ticket you purchase of the Lotto game consisting of picking 6 of 48 numbers is 1/12271512 or approximately 0.0000000815.
Learn more about the Permutations and Combinations at
https://brainly.com/question/4658834
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