Answer:
1 / 962598
Step-by-step explanation:
Let S be the sample space
total number of possible outcomes = n(S)
Let E be the event
total number of favorable outcomes = n(E)
Compute the number of ways to select 5 numbers from 0 through 42:
Total numbers to choose from = 43
So
Total number of ways to select 5 numbers from 43
= n(S) = 43C5
= 43! / 5! ( 43-5)!
= 43! / 5! 38!
= 43*42*41*40*39*38! / (5*4*3*2*1)*38!
= 115511760/120
n(S) = 962598
Hence there are 962598 ways to select 5 numbers from 43
Compute the probability of being a Big Winner
In order to be a Big Winner all 5 of the 5 winning balls are to be chosen and there is only one way you can for this event to occur. So
n(E) = 1
Here E is to be a Big Winner
So probability of being a Big Winner = P(E)
= n(E) / n(S)
= 1 / 962598
Hence
P(being a Big Winner) = P(E) = 1 / 962598
