Question

to win a lottery, 5 numbers are drawn at random from a pool of 61 numbers. numbers cannot repeat. if a person has one ticket, what is the probability that they have the winning ticket? the probability is □. (type an integer or fraction. simplify your answer.)

Explanation:

Step1: Calculate the combination of total cases

The formula for combination is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n = 61\) (total numbers) and \(r=5\) (numbers drawn).

$$C(61,5)=\frac{61!}{5!(61 - 5)!}=\frac{61\times60\times59\times58\times57}{5\times4\times3\times2\times1}=4686825$$

Step2: Calculate the probability

Since there is only 1 winning combination (the person's 1 ticket), the probability \(P=\frac{1}{C(61,5)}\)

Answer:

\(\frac{1}{4686825}\)