Question

In a certain lottery, there are ten balls, numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Of these, five are drawn in order. If you pick five numbers that match those drawn in the correct order, you win $1,000,000. What is the probability of winning such a lottery?

Short answer

The probability is$P=0.000033069$

Step-by-step solution

Step 1. Given Information

The given data is that there are ten balls, numbered 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Of these, five are drawn in order.

Step 2. Calculation

The number of ways in which we can choose 5 numbers out of 10 in order is given by $p(10,5)$

Use the formula of permutation to find the required probability,

$$\begin{gathered} p(n,r)=\frac{n!}{(n-r)!} \\ p(10,5)=\frac{10!}{(10-5)!} \\ =\frac{10·9·8·7·6·5!}{5!} \\ =30240 \end{gathered}$$

Thus, the probability of winning the lottery is as follows,

$$\begin{gathered} P=\frac{1}{30240} \\ P=0.000033069 \end{gathered}$$