Question

6. [-16 Points] DETAILS WANEFMAC7 8.4.030.NVA MY NOTES PRACTICE ANOTHER The Sad State Lottery requires you to select a sequence of three different numbers from 0 through 41. (Order is important.) You are a Winner if your sequence agrees with that in the drawing, and you are a Booby Prize Winner if your selection of numbers is correct, but in the wrong order. (Enter your answers as exact answers.) What is the probability of being a Winner? What is the probability of being a Booby Prize Winner? What is the probability that you are either a Winner or a Booby Prize Winner? Need Help? Watch It Talk to a Tutor

Answer 1

So we have to choose numbers from 42 numbers ( 0 -41 ) ,which can be done in $\binom{42}{3}$ ways .

Now, to be winner , the numbers chosen should be correct as well as correct in order . So there's only one way this can happen .  

So     $P[Winning] = \frac{1}{\binom{42}{3}}$

But , to be winner , the numbers need to be correct but the order not necessarily . Now 3 numbers can arrange themselves in 3! = 6 ways ; out of which 1 is the correct order.

So,  $P[Booby \ Winning] = \frac{3!-1}{\binom{42}{3}} = \frac{5}{\binom{42}{3}}$

P[Booby Winning or Winner] P[Booby winner] + P[Winner] - P[Booby winner n Winner] + 0-0 =