This is a series of posts that will focus on solving the daily problems posed by the user 
Mathematical Foundations
The probability of rolling n dice and getting all different numbers can be calculated using the following formula:P(all different) = (n! * (n - 1)!) / n^n
where:
- n is the number of dice
- ! represents the factorial (the product of all positive integers up to the given number)
In our case, for 6 dice, the formula would be:P(all different) = (6! * (6 - 1)!) / 6^6
Programming Foundations
To solve this problem in JavaScript, we can use the following functions:
- Factorial: A function that calculates the factorial of a number.
- Power: A function that calculates the power of a base number.
JavaScript Code// Function to calculate the factorial
function factorial(n) {
let result = 1;
for (let i = 1; i <= n; i++) {
result *= i;
}
return result;
}
// Function to calculate the probability
function probability(n) {
return (factorial(n) * factorial(n - 1)) / Math.pow(n, n);
}
// Print the probability for 6 dice
console.log(probability(6));
Output:0.879222863548825
Therefore, the probability of rolling 6 dice and getting all different numbers is approximately 87.9%.