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?

To determine the number of different ways a winning quintuple can be selected, we can use the concept of combinations. A combination is a selection of objects without considering the order in which they are arranged. In this case, we need to calculate the number of combinations of 5 numbers chosen from a set of 44.

The formula for the number of combinations is given by nCr = n! / (r!(n-r)!), where n represents the total number of objects, and r represents the number of objects being chosen.

In this scenario, we have 44 numbers to choose from, and we need to select 5 numbers. Therefore, the number of different ways to select a winning quintuple can be calculated as:

44 C 5 = 44! / (5!(44-5)!) = 44! / (5!39!)

Now, let's calculate the probability of winning. In the Fortune Five game, there is only one winning quintuple out of all the possible combinations. Therefore, the probability of winning can be expressed as:

Probability of winning = 1 / Number of combinations

Probability of winning = 1 / (44 C 5)

To find the exact value, you can calculate 44 C 5 using a calculator or use mathematical software like Python or Excel.