Question

solve the problem.
in a certain lottery, five different numbers between 1 and 20 inclusive are drawn. to win the lottery, a person must select the correct 5 numbers in the same order in which they were drawn. what is the probability of winning?
(1 point)
\\(\frac{120}{1,860,480}\\)
\\(\frac{1}{20!}\\)
\\(\frac{1}{1,860,480}\\)
\\(\frac{1}{120}\\)

Explanation:

Step1: Calculate the number of permutations

The formula for permutations \(P(n,r)=\frac{n!}{(n - r)!}\), where \(n = 20\) (total numbers) and \(r=5\) (numbers drawn).

$$P(20,5)=\frac{20!}{(20 - 5)!}=\frac{20!}{15!}=20\times19\times18\times17\times16 = 1,860,480$$

Step2: Calculate the probability

The probability \(P\) of winning is the ratio of the number of successful outcomes (which is \(1\) since there's only one correct sequence) to the total number of possible outcomes.

$$P=\frac{1}{1,860,480}$$

Answer:

\(\frac{1}{1,860,480}\) (the third option)