Question

When you toss a die while playing a game, you can get 1, 2, 3, 4, 5, or 6 on the top face. How many possible combinations of the top faces for the dice are there if:
a) you must toss 4 dice

b) you must toss n dice

Answer 1

Using the fundamental counting theorem, it is found that:

a) 1296 combinations are possible.

b) $6^n$ combinations are possible.

The fundamental counting theorem states that for n independents trials, each with $n_1, n_2, n_n$ ways of being done, the total number of combinations is:

$T = n_1 \times n_2 \times ... \times n_n$

Item a:

Four independent dice throws, each with six outcomes, thus:

$T = 6 \times 6 \times 6 \times 6 = 6^4 = 1296$

Item b:

n independent dice throws, each with six outcomes, thus:

$T = 6^n$

A similar problem is given at brainly.com/question/24067651