Question

In a certain lottery, five different numbers between 1 and 35 inclusive are drawn. These are the winning numbers. 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

Answer 1

`Pr =(1)/(38955840)`

Explanation:

Given

`n = 35` ---- 1 to 35

`r = 5` -- selection

Required

The probability of winning

The probability of getting the first number correctly is:

`P(1) = (1)/(35)`

At this point, the remaining numbers are 34

So, the second selection has the following probability

`P(2) = (1)/(34)`

Following the above sequence, we have:

`P(3) = (1)/(33)`

`P(4) = (1)/(32)`

`P(5) = (1)/(31)`

So, the required probability is:

`Pr =P(1) * P(2) * P(3) * P(4) * P(5)`

`Pr =(1)/(35) *(1)/(34)*(1)/(33)*(1)/(32)*(1)/(31)`

`Pr =(1)/(35*34*33*32*31)`

`Pr =(1)/(38955840)`