The probability of rolling a specific number on a die is 1/6. Since we want to roll 5 specific numbers in any order, we can use the formula for permutations:
P(n,r) = n! / (n-r)!
where n is the total number of items and r is the number of items we want to choose.
In this case, n = 6 (since there are 6 possible numbers on a die) and r = 5 (since we want to choose 5 specific numbers). So the number of permutations is:
P(6,5) = 6! / (6-5)! = 6! / 1! = 720
This means there are 720 possible ways to roll 5 different numbers on a die.
However, we only want to count the number of ways to roll the numbers 1, 2, 3, 4, and 5 in any order. There are 5! = 120 ways to arrange these numbers, so we need to multiply the total number of permutations by 120:
720 * 120 = 86,400
So the likelihood of rolling the numbers 1, 2, 3, 4, and 5 in some order when rolling 5 dice is 1 in 86,400, or approximately 0.001%.
What is the likelihood that when 5 die are rolled, that the numbers that turn up will be 1, 2, 3, 4, 5 in some order?
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