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
To find the number of possible combinations of the top faces of a die, you need to consider the number of choices for each die and multiply them together.
a) If you must toss 4 dice, there are 6 choices for each die (1, 2, 3, 4, 5, or 6). To find the total number of combinations, you multiply the number of choices for each die: 6 * 6 * 6 * 6 = 1296.
b) If you must toss n dice, the number of choices for each die is still 6. So, to find the total number of combinations, you multiply 6 by itself n times: 6^n.