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n list In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 43) and matching the number on the gold ball (1 through 32). If one ticket is purchased, what is the probability of winning the jackpot? The probability of winning the jackpot with one ticket is (Type an integer or a simplified fraction.)

n list\newlineIn one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (11 through 4343) and matching the number on the gold ball (11 through 3232). If one ticket is purchased, what is the probability of winning the jackpot?\newlineThe probability of winning the jackpot with one ticket is\newline(Type an integer or a simplified fraction.)

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Q. n list\newlineIn one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (11 through 4343) and matching the number on the gold ball (11 through 3232). If one ticket is purchased, what is the probability of winning the jackpot?\newlineThe probability of winning the jackpot with one ticket is\newline(Type an integer or a simplified fraction.)
  1. Calculate White Ball Combinations: To calculate the probability of winning the jackpot, we need to determine the total number of possible outcomes for the white balls and the gold ball.\newlineFor the white balls, since the order does not matter, we use the combination formula to find the number of ways to choose 55 distinct numbers out of 4343. The combination formula is C(n,k)=n!k!(n−k)!C(n, k) = \frac{n!}{k!(n-k)!}, where nn is the total number of items to choose from, kk is the number of items to choose, and ＂!＂ denotes factorial.
  2. Calculate Total Possible Outcomes: First, we calculate the number of combinations for the white balls: C(43,5)=43!5!(43−5)!=43!5!×38!=43×42×41×40×395×4×3×2×1C(43, 5) = \frac{43!}{5!(43-5)!} = \frac{43!}{5! \times 38!} = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1}
  3. Calculate Probability of Winning: Now, we perform the calculation for the white balls:\newlineC(43,5)=43×42×41×40×395×4×3×2×1=120,120C(43, 5) = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1} = 120,120\newlineSo, there are 120,120120,120 different combinations for the white balls.
  4. Calculate Probability of Winning: Now, we perform the calculation for the white balls: C(43,5)=43×42×41×40×395×4×3×2×1=120,120C(43, 5) = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1} = 120,120 So, there are 120,120120,120 different combinations for the white balls.Next, we calculate the number of possible outcomes for the gold ball. Since there is only one gold ball to be chosen out of 3232, there are 3232 possible outcomes.
  5. Calculate Probability of Winning: Now, we perform the calculation for the white balls:\newlineC(43,5)=43×42×41×40×395×4×3×2×1=120,120C(43, 5) = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1} = 120,120\newlineSo, there are 120,120120,120 different combinations for the white balls.Next, we calculate the number of possible outcomes for the gold ball. Since there is only one gold ball to be chosen out of 3232, there are 3232 possible outcomes.To find the total number of possible outcomes for both the white balls and the gold ball, we multiply the number of combinations for the white balls by the number of possible outcomes for the gold ball:\newlineTotal possible outcomes = 120,120120,120 (for white balls) ×32\times 32 (for gold ball)
  6. Calculate Probability of Winning: Now, we perform the calculation for the white balls:\newlineC(43,5)=43×42×41×40×395×4×3×2×1=120,120C(43, 5) = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1} = 120,120\newlineSo, there are 120,120120,120 different combinations for the white balls.Next, we calculate the number of possible outcomes for the gold ball. Since there is only one gold ball to be chosen out of 3232, there are 3232 possible outcomes.To find the total number of possible outcomes for both the white balls and the gold ball, we multiply the number of combinations for the white balls by the number of possible outcomes for the gold ball:\newlineTotal possible outcomes = 120,120120,120 (for white balls) ×32\times 32 (for gold ball)Now, we perform the calculation for the total possible outcomes:\newlineTotal possible outcomes = 120,120×32=3,843,840120,120 \times 32 = 3,843,840\newlineSo, there are 3,843,8403,843,840 different possible outcomes for both the white and gold balls.
  7. Calculate Probability of Winning: Now, we perform the calculation for the white balls:\newlineC(43,5)=43×42×41×40×395×4×3×2×1=120,120C(43, 5) = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1} = 120,120\newlineSo, there are 120,120120,120 different combinations for the white balls.Next, we calculate the number of possible outcomes for the gold ball. Since there is only one gold ball to be chosen out of 3232, there are 3232 possible outcomes.To find the total number of possible outcomes for both the white balls and the gold ball, we multiply the number of combinations for the white balls by the number of possible outcomes for the gold ball:\newlineTotal possible outcomes = 120,120120,120 (for white balls) ×32\times 32 (for gold ball)Now, we perform the calculation for the total possible outcomes:\newlineTotal possible outcomes = 120,120×32=3,843,840120,120 \times 32 = 3,843,840\newlineSo, there are 3,843,8403,843,840 different possible outcomes for both the white and gold balls.The probability of winning the jackpot with one ticket is the reciprocal of the total number of possible outcomes, since there is only one winning outcome.\newlineProbability of winning = 1Total possible outcomes\frac{1}{\text{Total possible outcomes}}
  8. Calculate Probability of Winning: Now, we perform the calculation for the white balls:\newlineC(43,5)=43×42×41×40×395×4×3×2×1=120,120C(43, 5) = \frac{43 \times 42 \times 41 \times 40 \times 39}{5 \times 4 \times 3 \times 2 \times 1} = 120,120\newlineSo, there are 120,120120,120 different combinations for the white balls.Next, we calculate the number of possible outcomes for the gold ball. Since there is only one gold ball to be chosen out of 3232, there are 3232 possible outcomes.To find the total number of possible outcomes for both the white balls and the gold ball, we multiply the number of combinations for the white balls by the number of possible outcomes for the gold ball:\newlineTotal possible outcomes = 120,120120,120 (for white balls) ×32\times 32 (for gold ball)Now, we perform the calculation for the total possible outcomes:\newlineTotal possible outcomes = 120,120×32=3,843,840120,120 \times 32 = 3,843,840\newlineSo, there are 3,843,8403,843,840 different possible outcomes for both the white and gold balls.The probability of winning the jackpot with one ticket is the reciprocal of the total number of possible outcomes, since there is only one winning outcome.\newlineProbability of winning = 1Total possible outcomes\frac{1}{\text{Total possible outcomes}}Finally, we calculate the probability of winning the jackpot with one ticket:\newlineProbability of winning = 13,843,840\frac{1}{3,843,840}

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