1. There are 6 possible outcomes for each roll, so there are 6^n possible sequences of n rolls.
2. If we want to have all even numbers, we can only roll 2, 4, or 6 on each roll. So there are 3 options for each roll, and the total number of sequences consisting entirely of even numbers is 3^n.
3. If the first, third, and fourth numbers must be the same, we can treat them as one roll and ignore them in the count of possible sequences. So we have 6 options for the first, third, and fourth numbers, and 6 options for the second and fifth numbers, giving us a total of 6^3 * 6^2 = 6^5 possible sequences.
fair
-sided die is rolled
times and the resulting sequence of
numbers is recorded.
How many different sequences are possible?
How many different sequences consist entirely of even numbers?
How many different sequences are possible if the first, third, and fourth numbers must be the same?
3 answers
A fair 6-sided die is rolled 4times and the resulting sequence of 4numbers is recorded.
A park bench can seat 3 people. How many seating arrangements are possible if 3 people out of a group of 12 want to sit on the park bench?
3 answers