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The arithmetic mean is the sum divided by the number of terms:
Alex rolls two fair 12-sided dice, each numbered from 1 to 12. What is the probability that the sum of the numbers rolled is exactly 15?
To find the probability that the sum of the numbers rolled on two 12-sided dice is 15, we first determine the total number of possible outcomes and then count the favorable outcomes.
The probability is the number of favorable outcomes divided by the total number of outcomes:
To calculate the number of passwords with the letter A included, we use combinatorial selection:
A gardener has 3 types of flowers: 4 roses, 3 daisies, and 2 tulips. If the gardener wants to plant them in a row such that all flowers of the same type are indistinguishable, how many different arrangements are possible?
To find the number of distinct arrangements of the flowers, we use the formula for permutations of multiset:
A remote research station in the Arctic has 6 distinct experiments to be conducted over 3 days, with 2 experiments each day. How many ways can the experiments be scheduled if the order of experiments within a day does not matter?
This problem involves partitioning 6 distinct experiments into 3 groups of 2, where the order of groups (days) does not matter:
The number of ways to choose 2 experiments out of 6 is: