5 dice will be thrown one by one, then the product of the 5 numbers will be counted. Which will be higher, the product probability of 180 or the product probability of 144?
This is my attempt at this one:
180 = 2 x 2 x 3 x 3 x 5 =15 - This is the sum of the prime factors of 180.
This one has : 5! /2!2! =30 permutations
So, 30 / 120 = 1/4 = 25 % probability
144 =4 x 2 x 2 x 3 x 3 = 14 - This is one of the the sums of the prime factors of 144.
144 =2 x 2 x 2 x 3 x 6 = 15 - This is the other possible sum of the prime factors of 144.
The first one has : 5! / 2!2! = 30 permutations
The 2nd one has : 5! / 3! = 20 permutations
And this one has : [30 + 20] /120 =41.667% probability
Therefore, the product probability of 144 > 180.
P. S. For goodness sake, some mathematician should check this !!! Thanks.
