I have been able to figure out everything on my assignment but this one. Can anyone help?
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?
The number of ways to choose 5 out of 44 numbers is
C(44,5) = 44!/(5!39!) = 1086008
So the prob of winning is 1/1086008
Thank you, now I feel really dumb. Ive been pondering this question for an hour or two.
A blueprint for a museum uses a scale of a 1/4 in:1ft. One of the rooms on the blueprint is 3 3/4 in. long. How long is the actual room?
3 3/4in -> 15/4 -> 3.75
0.25 in. 3.75
-------- = ------- Now cross multiply
1ft. X
X= 15ft
To determine the number of different ways a winning quintuple can be selected, we need to use the concept of combinations. In this case, we need to choose 5 numbers out of the 44 available without considering the order of the numbers.
The formula to calculate combinations is nCr, where n is the total number of items to choose from and r is the number of items to be selected.
In this scenario, we have 44 numbers to choose from (n = 44) and we want to select a quintuple (r = 5). Therefore, the number of different ways to select a winning quintuple is:
44C5 = 44! / (5! * (44-5)!)
= 44! / (5! * 39!)
= (44 * 43 * 42 * 41 * 40) / (5 * 4 * 3 * 2 * 1)
= 1,086,008
So, there are 1,086,008 different ways to select a winning quintuple in the Fortune Five game of the state lottery.
Now, to calculate the probability of winning, we need to consider the total number of possible outcomes. Since we're picking 5 numbers from a set of 44, the total number of possible outcomes is given by:
44C5 = 1,086,008
The probability of winning can be calculated by dividing the number of ways to win (1,086,008) by the total number of possible outcomes (1,086,008):
Probability of winning = 1,086,008 / 1,086,008 = 1
Therefore, the probability of winning is 1, or 100%.