Using the fundamental counting theorem, it is found that:
a) 1296 combinations are possible.
b) [tex]6^n[/tex] combinations are possible.
The fundamental counting theorem states that for n independents trials, each with [tex]n_1, n_2, n_n[/tex] ways of being done, the total number of combinations is:
[tex]T = n_1 \times n_2 \times ... \times n_n[/tex]
Item a:
Four independent dice throws, each with six outcomes, thus:
[tex]T = 6 \times 6 \times 6 \times 6 = 6^4 = 1296[/tex]
Item b:
n independent dice throws, each with six outcomes, thus:
[tex]T = 6^n[/tex]
A similar problem is given at https://brainly.com/question/24067651
