To determine the probability of winning the jackpot in the SuperLottery, we will first calculate the total number of ways to select the balls and then the number of winning selections.
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Choosing the white balls: We need to choose 3 balls from a total of 10 white balls. The number of ways to choose 3 balls from 10 can be calculated using the binomial coefficient, given by:
\[ \binom{10}{3} = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120. \]
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Choosing the SuperBall: There is only 1 SuperBall selected from 10 possible balls (numbered from 11 to 20). Thus, the number of ways to choose the SuperBall is simply:
\[ \binom{10}{1} = 10. \]
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Total combinations of drawing the balls: The total number of possible combinations of the lottery draw (3 white balls and 1 SuperBall) can be calculated by multiplying the combinations of the white balls and the SuperBall:
\[ \text{Total combinations} = \binom{10}{3} \cdot \binom{10}{1} = 120 \times 10 = 1200. \]
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Winning combinations: To win the jackpot, all selected numbers on the ticket must match the drawn balls. There is exactly 1 way to win, which is by matching the specific combination of the 3 white balls and the 1 SuperBall drawn.
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Calculating the probability: The probability of winning can be expressed as the fraction of winning combinations to the total combinations:
\[ P(\text{win}) = \frac{\text{Winning combinations}}{\text{Total combinations}} = \frac{1}{1200}. \]
Thus, the probability that you win the jackpot is
\[ \boxed{\frac{1}{1200}}. \]
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