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
a) To determine the number of possible combinations when tossing 4 dice, we can use the concept of permutations.
When tossing a single die, there are 6 possible outcomes (1, 2, 3, 4, 5, or 6). Since there are 4 dice being tossed, each die has 6 possible outcomes. Therefore, the total number of possible combinations is obtained by multiplying the number of outcomes for each die together: 6 * 6 * 6 * 6 = 6^4 = 1296.
So, when tossing 4 dice, there are 1296 possible combinations for the top faces.
b) To calculate the number of possible combinations when tossing n dice, we again use the concept of permutations.
Since each die has 6 possible outcomes, we need to raise 6 to the power of n (6^n) to determine the total number of combinations for n dice.
So, when tossing n dice, there are 6^n possible combinations for the top faces.