lokiisnotdead

ok now subtract that from the total since we are complementary counting (I'm assuming you know what that means)

i replied back :)

and then subtract that from the total.

ok so yea there are 9 cases with the superball. now just multiply 9 with the other 2 cases in my previous post.

hi guest!

this sequence has a common divisor of 7. So that means that the next terms is 16807*7=117,649.

i'm confused, which part of it is wrong?

hi guest!

so i see that this is an aops problem, so I'll only give you some hints.

there are \(\dbinom{10}{3}\cdot10=1200\) total possibilities. 

since there are many cases to how you could win, its best to use complementary counting in this case. So, to have a losing ticket, you must have at most one correct white ball, and miss the superball.

1. Missing all 3 white balls: this happens if your ticket contains 3 of the 7 white numbers that weren't drawn, so there are \(\dbinom{7}{3}=35\) possibilities for that situation.

2. If you hit 1 white ball and miss the others: this happens if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 7 white numbers that weren't drawn, so there are \(3\dbinom{7}{2}=63\) possibilities for that case. 

from here, all you have to calculate are the cases with the superball and subtract them from the total since we are complementary counting.

i think you can do the rest from there!

you got this!

ask me if you need any more help!

:)

hi guest!

so the problem is:

In the SuperLottery, three balls are drawn (at random) from ten white balls numbered from 1 to 10, and one SuperBall is drawn (at random) from ten red balls numbered from 11 to 20. When you buy a ticket, you choose three numbers from 1 to 10, and one number from 11 to 20. If the numbers on your ticket match at least two of the white balls or match the red SuperBall, then you win a super prize. What is the probability that you win a super prize?

i see that it's an aops problem, so I'll only give you some hints.

there are \(\dbinom{10}{3}\cdot 10=1200\) total possibilities. 

since there are many cases to how you could win, its best to use complementary counting in this case. So, to have a losing ticket, you must have at most one correct white ball, and miss the superball.

1. Missing all 3 white balls: this happens if your ticket contains 3 of the 7 white numbers that weren't drawn, so there are \(\dbinom{7}{3}=35\) possibilities for that situation.

2. If you hit 1 white ball and miss the others: this happens if your ticket contains 1 of the 3 white numbers that were drawn and 2 of the 7 white numbers that weren't drawn, so there are \(3\dbinom{7}{2}=63\) possibilities for that case. 

from here, all you have to calculate are the cases with the superball and subtract them from the total since we are complementary counting.​

i think you can do the rest from there!

you got this!

ask me if you need any more help!

:)

hi guest!

you can either factor or use the quadratic formula.

in this case, I'll use the quadratic formula.

The formula is: \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)

So, you can just plug the values in. In this case: a=1, b=6, c=25

i think you can do the rest by yourself!

you got this!

:)

\(z=2, -1+\sqrt{3}i,-1-\sqrt{3}i\)