A daily lottery is conducted in which two winning numbers are selected out of 100 numbers. How many different combinations of winning numbers are possible?
4950
P = 100!/(2!)(100-2)! = 100!/(2)(98!) = 100*99/2 = 9900/2 = ?
There are 100 numbers in the lottery and 2 numbers are selected, so it's just like picking your favorite pair of socks from a drawer full of socks. Each selection is independent, so to find the number of different combinations, we need to use a little bit of math magic.
Now, imagine you are trying to juggle 100 balls, and you can only juggle two at a time. Each juggle is a separate combination! So, we need to find the number of ways to juggle two balls in a sea of 100.
Using a bit of mathematical hocus pocus, we can apply the "n choose k" formula, where n is the total number of balls (in this case, 100) and k is the number of balls we want to juggle (in this case, 2).
Applying the formula, we find that the number of different combinations of winning numbers is:
100 choose 2 = (100!)/(2!(100-2)!) = 100 * 99 / 2 = 4950
So, there are 4950 different combinations of winning numbers in this daily lottery! Good luck juggling those balls!
To determine the number of different combinations of winning numbers, we can use the concept of combinations. In this case, we want to select 2 numbers out of 100 numbers.
The formula for combinations is C(n, r) = n! / (r! * (n - r)!), where n represents the total number of objects and r represents the number of objects being chosen.
In this scenario:
- n = 100 (as we have 100 numbers to choose from)
- r = 2 (as we want to select 2 winning numbers)
Therefore, the number of different combinations of winning numbers is:
C(100, 2) = 100! / (2! * (100 - 2)!)
= 100! / (2! * 98!)
= (100 * 99) / (2 * 1)
= 4950
So, there are 4950 different combinations of winning numbers possible in this daily lottery.
To find the number of different combinations of winning numbers, we need to use the concept of combinations. In this case, we are selecting two numbers out of 100.
The formula to calculate the number of combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
C = the number of combinations
n = the total number of items (in this case, 100 numbers)
r = the number of items chosen (in this case, 2 numbers)
! = factorial (which means multiplying a number by all the positive integer numbers less than it)
Plugging in the values into the formula:
C(100, 2) = 100! / (2!(100-2)!)
Now, let's simplify the formula:
C(100, 2) = (100 * 99 * 98 * ... * 3 * 2 * 1) / (2 * 1 * (98 * 97 * ... * 3 * 2 * 1))
Many terms cancel out:
C(100, 2) = (100 * 99) / (2 * 1)
C(100, 2) = 4950
Therefore, there are 4950 different combinations of winning numbers possible in this daily lottery.