In a certain lottery, 3 different numbers between 1 and 13 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn is unimportant.
To find the number of different selections, we need to find the number of combinations of 3 numbers that can be drawn from a set of 13 numbers.
The formula for combinations is given by nCr = n! / (r!(n-r)!),
where n is the total number of elements in the set and r is the number of elements to be chosen.
In this case, we have 13 numbers to choose from and we want to choose 3 numbers.
So the number of different selections is 13C3 = 13! / (3!(13-3)!)
Simplifying this expression, we get:
13! / (3!10!)
= (13 * 12 * 11) / (3 * 2 * 1)
= 286
So there are 286 different selections possible in this lottery.