Recall the formula for a number of combinations of n objects taken r at a time, where r ≤ n.
1/15 890 700
Practice makes perfect
We want to find the probability of winning a lottery. To do so we will use theoretical probability.
P=Favorable Outcomes/Possible Outcomes
We will start by finding the number of possible outcomes. We assume that lottery numbers are selected at random and the order is not important. We are choosing among integers from 0 to 49. Therefore, there are total of 50 numbers to choose from.
From 0 to 49 ⇒ 50 integers
The number of possible outcomes will be the number of combinations of 50 numbers taken 6 at the time. This is because in order to win we must correctly select 6 numbers. Let's recall the formula for the number of combinations of n objects taken r at a time, where r ≤ n.
_nC_r = n!/(n-r)! * r!
In our case, the total number integers from which we can choose is 50, so n = 50. Out of them, we select 6, so we know that r = 6. Let's substitute these values and find the number of possible combinations.
The number of possible outcomes is 15 890 700. Next, we will look for the number of favorable outcomes. There is only one combination of numbers that guarantees winning in the lottery, so the number of favorable outcomes is 1. We are ready to calculate the desired probability.
P=Favorable Outcomes/Possible Outcomes [0.9em]
⇕
P=1/15 890 700
The probability of winning the lottery is 115 890 700.
