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 any different ways can a winning quintuple be selected? What is the probability of winning?
1/44 x 1/43 x 1/42 x 1/41 x 1/40 = 1/130,320,860
1 in 130.3 million is the probability
To find the number of different ways a winning quintuple can be selected, we can use the concept of combinations. In this case, we want to find the number of ways to choose 5 numbers out of 44, without repetition.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
where C(n, r) represents the number of ways to choose r items out of n, and "!" denotes factorial.
In our case, n = 44 (total numbers to choose from) and r = 5 (numbers to be selected).
Plugging these values into the formula, we get:
C(44, 5) = 44! / (5!(44-5)!)
Simplifying,
C(44, 5) = 44! / (5!39!)
Now we can calculate this using a calculator or a mathematical software. The resulting answer will give us the number of different ways to select a winning quintuple.
Once we have calculated the number of different ways, we can find the probability of winning by dividing the number of winning quintuples by the total number of possible combinations.
The total number of possible combinations is given by C(44,5). So, the probability of winning can be calculated as:
Probability of Winning = Number of Winning Quintuples / Total Number of Combinations
By simplifying the above expression, the probability of winning can be found.