Winning the jackpot in a particular lottery requires that you select the correct four numbers betwee separate drawing, you must also select the correct single number between 1 and 48 . Find the prob the jackpot. The probability of winning the jackpot is (Type an integer or simplified fraction.)

To find the probability of winning the jackpot in the lottery, we need to consider both parts of the selection process: selecting the correct four numbers and selecting the correct single number. 1. **Selecting the correct four numbers**: Assuming that the four numbers are chosen from a set of numbers (let's say from 1 to 49), the number of ways to choose 4 numbers from 49 can be calculated using the combination formula: \[ \text{Number of combinations} = \binom{n}{k} = \frac{n!}{k!(n-k)!} \] where \( n \) is the total number of options (49 in this case) and \( k \) is the number of selections (4). \[ \binom{49}{4} = \frac{49!}{4!(49-4)!} = \frac{49 \times 48 \times 47 \times 46}{4 \times 3 \times 2 \times 1} = 2118760 \] 2. **Selecting the correct single number**: There are 48 possible choices for the single number (from 1 to 48). 3. **Calculating the total number of outcomes**: The total number of outcomes for winning the jackpot is the product of the number of ways to choose the four numbers and the number of ways to choose the single number: \[ \text{Total outcomes} = \binom{49}{4} \times 48 = 2118760 \times 48 = 101313280 \] 4. **Calculating the probability of winning the jackpot**: The probability of winning the jackpot is the reciprocal of the total number of outcomes: \[ P(\text{winning}) = \frac{1}{\text{Total outcomes}} = \frac{1}{101313280} \] Thus, the probability of winning the jackpot is: \[ \frac{1}{101313280} \] This is the simplified fraction representing the probability of winning the jackpot.