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?

Guest Jan 7, 2020

#1**0 **

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.

Guest Jan 7, 2020

edited by
Guest
Jan 7, 2020

edited by Guest Jan 7, 2020

edited by Guest Jan 7, 2020