Question

Predict the number of outcomes for the given number of rolls:
Outcome: 3
Number of rolls: 36

Answer 1

To determine the number of outcomes when rolling a die multiple times, we can use the formula for the number of outcomes in terms of rolls and sides of the die.

If we assume a standard six-sided die (which has 6 outcomes for each roll), the total number of outcomes when rolling the die \( n \) times is given by:

\[
\text{Total Outcomes} = (\text{Number of outcomes per roll})^{\text{Number of rolls}}
\]

For a six-sided die:
- Number of outcomes per roll = 6
- Number of rolls = 36

Now we can calculate the total outcomes:

\[
\text{Total Outcomes} = 6^{36}
\]

This expression \( 6^{36} \) gives us the total number of different outcomes possible when rolling a die 36 times.

Now, let's calculate \( 6^{36} \):

\[
6^{36} \approx 2.17678 \times 10^{28}
\]

Therefore, the total number of outcomes when rolling a six-sided die 36 times is approximately \( 2.17678 \times 10^{28} \).