Answer :
Using the arrangements formula, it is found that there are 72 distinct four-digit positive integers are such that the product of their digits equals 12.
What is the arrangements formula?
The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, considering that the numbers are arranged, we have that there are:
- 4! 4-digit numbers involving a six, a two and two ones that result in a product of 12.
- 4! 4-digit numbers involving a four, a three and two ones that result in a product of 12.
- 4! 4-digit numbers involving a three , two twos and a one that result in a product of 12.
Hence:
T = 3 x 4! = 3 x 24 = 72.
There are 72 distinct four-digit positive integers are such that the product of their digits equals 12.
More can be learned about the arrangements formula at https://brainly.com/question/24648661