Find the probability of winning the lottery
Select the six winning numbers from 1 to 34. (in any order, no repeats)
P(winning)= ?
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To find the probability of winning the lottery, we need to determine the number of ways to win and the total number of possible outcomes.
Step 1: Determine the number of ways to win
In this case, we need to select six winning numbers from 1 to 34 (in any order, with no repeats). This can be solved using the concept of combinations. The number of ways to select six numbers from a pool of 34 without considering the order is given by the formula: C(n, r) = n! / (r! * (n-r)!), where n is the total number of objects to choose from, and r is the number of objects to choose. In this case, n = 34 (the total number of numbers) and r = 6 (the number of numbers to choose). So, the number of ways to win is C(34, 6).
Step 2: Determine the total number of possible outcomes
Since we are selecting six numbers from a pool of 34 numbers, the total number of possible outcomes is given by the formula: C(n, r), where n = 34 (the total number of numbers) and r = 6 (the number of numbers to choose). So, the total number of possible outcomes is C(34, 6).
Step 3: Calculate the probability of winning
The probability of winning is the number of ways to win divided by the total number of possible outcomes. So, the probability of winning is:
P(winning) = (number of ways to win) / (total number of possible outcomes)
P(winning) = C(34, 6) / C(34, 6)
To calculate these combinations, we need to evaluate the factorials:
C(34, 6) = 34! / (6! * (34-6)!)
C(34, 6) = 34! / (6! * 28!)
Now, we can calculate the probability of winning the lottery.