A certain lottery is won by selecting the correct four numbers from 1,2....30. The probability of winning if the rules are changed so that in addition to selecting the correct four numbers you must now select them in the same order as they are drawn?
In order to solve this probability problem, we need to count the number of favorable outcomes and the total number of possible outcomes.
First, let's calculate the total number of possible outcomes when drawing four numbers from 1 to 30. Since each number can only be selected once and the order doesn't matter, we can use the combination formula.
The total number of possible outcomes is given by:
Total number of outcomes = nCr(30, 4) = 30! / (4! * (30-4)!),
where nCr denotes the combination function.
Using this formula, we find that there are 27,405 possible outcomes.
Next, let's calculate the number of favorable outcomes, which in this case means selecting the correct four numbers in the same order as they are drawn.
Since we need to choose the numbers in the specific order they are drawn, the first number has only one possibility, the second number has one possibility (since we've already selected one), and so on.
Therefore, the number of favorable outcomes is simply 1.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes.
In this case, the probability is:
Probability = 1 / 27,405 ≈ 0.00003648.
So, the probability of winning the lottery when the rules are changed to selecting the correct four numbers in the same order is approximately 0.00003648, or about 0.003648%.