Five numbers are to be picked, without repetition, from 44 numbers to determine the winner of the Fortune Five game in the state lottery. If the order of the numbers is insignificant, how many different ways can a winning quintuple be selected? What is the probability of winning?
number of ways to it can be selected
44*43*42*41*40
number of ways
130320960
Number of ways you could pick this number
5*4*3*2*1
120
Probability of winning
120/130320960
.0000921%
Am I right?
Thank you!
1086008
First, let's calculate the number of different ways a winning quintuple can be selected. Since there are 44 numbers to choose from and without repetition, we can use the multiplication principle. So, the number of ways to select the numbers is:
44 * 43 * 42 * 41 * 40 = 3,686,880
So, there are 3,686,880 different ways to select a winning quintuple.
Next, let's calculate the probability of winning. The probability is the number of favorable outcomes (winning quintuples) divided by the number of possible outcomes. In this case, the number of favorable outcomes is 1 (since we can only win with one specific quintuple), and the number of possible outcomes is 3,686,880.
Therefore, the probability of winning is:
1 / 3,686,880 ≈ 0.0000002710573
Converting this probability to a percentage gives:
0.0000002710573 * 100 ≈ 0.00002710573%
So, the probability of winning is approximately 0.00002710573%.
Hence, the probability you calculated (.0000921%) is incorrect. The correct probability is approximately 0.00002710573%.