Complete Question
Find the probability of winning a lottery with the following rule. Select the six winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Answer:
The probability is ![P(winning ) = 7.435 *10^{-7}](https://tex.z-dn.net/?f=P%28winning%20%29%20%3D%20%207.435%20%2A10%5E%7B-7%7D)
Step-by-step explanation:
From the question we are told that
The total winning numbers n = 34
The total number to select is r = 6
The total outcome of lottery is mathematically represented as
![t_{outcome}) = \left n } \atop {}} \right. C_r](https://tex.z-dn.net/?f=t_%7Boutcome%7D%29%20%3D%20%20%5Cleft%20n%20%7D%20%5Catop%20%7B%7D%7D%20%5Cright.%20C_r)
![t_{outcome}) = \frac{n! }{(n-r )! r!}](https://tex.z-dn.net/?f=t_%7Boutcome%7D%29%20%3D%20%20%5Cfrac%7Bn%21%20%7D%7B%28n-r%20%29%21%20r%21%7D)
substituting values
![t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}](https://tex.z-dn.net/?f=t_%7Boutcome%7D%29%20%3D%20%20%5Cfrac%7B%2034%20%21%20%20%7D%7B%2834%20-%206%20%20%29%21%206%21%7D)
![t_{outcome}) = \frac{ 34 ! }{28 ! 6!}](https://tex.z-dn.net/?f=t_%7Boutcome%7D%29%20%3D%20%20%5Cfrac%7B%2034%20%21%20%20%7D%7B28%20%21%206%21%7D)
![t_{outcome}) =1344904](https://tex.z-dn.net/?f=t_%7Boutcome%7D%29%20%3D1344904)
The number of desired outcome is
![t_{desired} = 1](https://tex.z-dn.net/?f=t_%7Bdesired%7D%20%20%3D%201)
this is because the desired outcome is choosing the six winning number
The probability of winning a lottery is mathematically represented as
![P(winning ) = \frac{t_{desired}}{t_{outcome}}](https://tex.z-dn.net/?f=P%28winning%20%29%20%3D%20%20%5Cfrac%7Bt_%7Bdesired%7D%7D%7Bt_%7Boutcome%7D%7D)
substituting values
![P(winning ) = \frac{1}{1344904 }](https://tex.z-dn.net/?f=P%28winning%20%29%20%3D%20%20%5Cfrac%7B1%7D%7B1344904%20%7D)
![P(winning ) = 7.435 *10^{-7}](https://tex.z-dn.net/?f=P%28winning%20%29%20%3D%20%207.435%20%2A10%5E%7B-7%7D)