A state lottery involves the random selection of six different numbers between 1 and 25. If you select one six number combination, what is the probability that it will be the winning combination?a.1/720b.1/127,512,000c.1/177,100d.1/244,140,625

The probability that a six number combination selected is the winning combination [tex]\boxed{\frac{1}{{127512000}}}[/tex]. Further Explanation:Probability can be defined as the ratio of favorable number of outcomes to the total number of outcomes. Given:There are [tex]25[/tex] numbers from one to twenty five Concept used:The probability [tex]P\left( E \right)[/tex] of any event [tex]E[/tex] can be calculated as, [tex]P\left( E \right) = \dfrac{{n\left( E \right)}}{{n\left( S \right)}}[/tex] Here, [tex]n\left( E \right)[/tex] is the total number of elements in event [tex]E[/tex] and [tex]n\left( S \right)[/tex] is the number of element in sample space of an experiment. Calculation: The probability that the first digit of lottery number is same as picked can be calculated as, [tex]P\left( 1 \right) = \dfrac{1}{{25}}[/tex]The probability that the second digit of lottery number is same as picked can be calculated as, [tex]P\left( 2 \right) = \dfrac{1}{{24}}[/tex]The probability that the third digit of lottery number is same as picked can be calculated as, [tex]P\left( 3 \right) = \dfrac{1}{{23}}[/tex]The probability that the fourth digit of lottery number is same as picked can be calculated as, [tex]P\left( 4 \right) = \dfrac{1}{{22}}[/tex]The probability that the fifth digit of lottery number is same as picked can be calculated as, [tex]P\left( 5 \right) = \dfrac{1}{{21}}[/tex]The probability that the sixth digit of lottery number is same as picked can be calculated as, [tex]P\left( 6 \right) = \dfrac{1}{{20}}[/tex]The probability that the all digit of lottery number is same as picked can be calculated as, [tex]\begin{aligned}P &= \frac{1}{{25}} \times \frac{1}{{24}} \times \frac{1}{{23}} \times \frac{1}{{22}} \times \frac{1}{{21}} \times \frac{1}{{20}} \\ &= \frac{1}{{127512000}} \\ \end{gathered}[/tex]The probability that a six number combination selected is the winning combination [tex]\boxed{\frac{1}{{127512000}}}[/tex]. Hence, [tex]\boxed{{\text{Option b}}}[/tex] is correct. Learn more: 1. Learn more about unit conversion 2. Learn more about non-collinear 3. Learn more about inverse of function Answer details: Grade: High School Subject: Mathematics Chapter: Probability Keywords: Probability, outcome, total number of outcomes, ratio, favorable number of outcomes, lottery, digit, number, winning, combination, select, six numbers, randomly select.