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?
There will be C(44,5) ways to choose 5 numbers from 44 or 44!/(5!39!) or
1086008 ways
so the prob of winning is 1/1086008
if 89,88,45,9,33, were selected from 1-90, what are the five numbers which will be selected next.
To find the number of different ways a winning quintuple can be selected, we can use the concept of combinations. In this case, we have 44 numbers to choose from and we want to select 5 numbers without repetition. The order of the numbers is insignificant, which means that different sequences of the same numbers are considered the same combination.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items to be chosen.
In this case, we have:
n = 44 (the total number of numbers)
r = 5 (the number of numbers to be chosen)
Using the formula, we can calculate the number of different ways to select a winning quintuple:
C(44, 5) = 44! / (5!(44-5)!) = 44! / (5!39!)
Now let's calculate the probability of winning. The probability of winning is the ratio of the number of favorable outcomes (which is the number of different ways to select a winning quintuple) to the total number of possible outcomes.
The total number of possible outcomes is the number of ways to select any quintuple from the 44 numbers:
C(44, 5) = 44! / (5!39!)
So, the probability of winning is:
Probability of winning = Number of favorable outcomes / Total number of possible outcomes
Probability of winning = C(44, 5) / C(44, 5)
Simplifying this expression, we find:
Probability of winning = 1
Therefore, the probability of winning the Fortune Five game in the state lottery is 1, which means that if you play, you will definitely win.