Solve the problem
In a certain lottery, 5 different numbers between 1 and 10 inclusive are drawn at random. These are the winning numbers. If you choose 5 different numbers at random between 1 and 10, what is the probability you will match the winning numbers. Assume that the order of the numbers is unimportant
In fraction form
To solve this problem, we need to find the number of favorable outcomes (matching the winning numbers) and the number of total possible outcomes.
The number of possible outcomes for choosing 5 different numbers at random between 1 and 10 is given by the combination formula:
nCr = n! / (r! * (n-r)!)
In this case, n = 10 (total numbers to choose from) and r = 5 (number of numbers to choose). Plugging in the values, we get:
10C5 = 10! / (5! * (10-5)!)
= 10! / (5! * 5!)
= (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)
= 252
So, the total number of possible outcomes is 252.
Now, let's calculate the number of favorable outcomes. Since we are matching the winning numbers, we can choose any 5 numbers from the winning numbers.
The number of ways to choose 5 different numbers from the winning numbers is given by the combination formula:
5C5 = 5! / (5! * (5-5)!)
= 5! / (5! * 0!)
= (5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1)
= 1
So, there is only 1 favorable outcome.
Therefore, the probability of matching the winning numbers is:
Probability = Favorable outcomes / Total possible outcomes
= 1 / 252
Hence, the probability you will match the winning numbers is 1/252 in fraction form.