Consider the following game: A drum contains 10 balls, each numbered from 1 to 10. Three balls are randomly drawn, without replacement, from the drum. Prior to the draw, you fill out a card by selecting three numbers from 1 to 10. To win a prize, the numbers you select have to correspond to the numbers of the balls drawn, in any order. What is the probability of winning a prize?

Answer: 1/120

Step-by-step explanation: First to calculate the probability, we must know the possible number of way that 3 balls can be drawn from 10 balls numbered 1-10, and the number of ways that the 3 numbers selected from the player will match the number the numbers that the player chose.

To get the total number of outcomes this entails 10C3

From the formula nCr = n! / (r! (n-r) !)

10C3 = 10! / (3! (10-3) !)

10! = 10*9*8*7*6*5*4*3*2*1 = 3628800

3! = 3*2*1 = 6

(10-3) ! = 7! = 7*6*5*4*3*2*1 = 5040

10C3 = 3628800 / (6*5040) = 120

Of all the 120 outcomes possible, only one outcome is expected to match all the 3 numbers that the player had written down, hence the probability for winning the draw will be

3C3/10C3

=1/120 = 0.0083333333333