Choose the probability as a fraction in lowest terms
a.5/164490480
b.5/1370754
c.1/1370754
d.1/164490480
determine probability of winning a lottery from which 5 numbers are drawn without replacement from the set of numbers 1 to 46. in order to win, the 5 numbers must be selected in the same order in which they are drawn.
1/46 * 1/45 * 1/44 * 1/43 * 1/42
= 1 / 164490480
Thank you
To determine the probability of winning a lottery where 5 numbers are drawn without replacement from the set of numbers 1 to 46, we can use the concept of combinations.
The total number of possible outcomes, or combinations, can be calculated using the formula for combinations:
nCr = n! / (r!(n-r)!)
where n is the total number of items (46 in this case) and r is the number of items being chosen (5 in this case).
So, the total combinations of selecting 5 numbers out of 46 without replacement is:
46C5 = 46! / (5!(46-5)!)
Simplifying this expression:
46C5 = 46! / (5! x 41!)
Now, to calculate the probability of winning, we need to determine the number of favorable outcomes, which in this case is winning the lottery by selecting the 5 numbers in the same order as they are drawn. There is only 1 favorable outcome.
Therefore, the probability of winning the lottery is:
Probability = favorable outcomes / total outcomes
Probability = 1 / 46C5
To express this probability as a fraction in lowest terms, we need to simplify it further:
46C5 = 46! / (5! x 41!) = 164490480
So, the probability in lowest terms is:
1 / 164490480
Therefore, the correct answer is d) 1/164490480.