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.
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
1 answer