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.

Answer 1

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.