A summation of all the probabilities related to a given event equals 1 and can be expressed as:
Combination:
a calculation where we find the number of ways to take r items from a population of n things without regard to order. There are a number of ways to notate this. I'll use
Counting Principle:
when there are a certain number of ways to do one thing (like roll a die) and an unrelated number of ways to do another thing (like flip a coin), we multiply the two ways together to see the number of results possible
Factorial:
a calculation where we take all the natural numbers up to and including the nth number and multiplying them together. The notation is an exclamation mark. For instance, 4! is 4 X 3 X 2 X 1 = 24. In general, n! = 1 X 2 X ... (n-1) X n.
Mean:
a calculation where we take the sum of a list of values and divide by the number of those values (the count).
Partition:
a calculation where we find all the unique combinations of ways to add up to a given whole number (we include the number itself + 0). For example, the partition of 5 is 7: 5, 4+1, 3+2, 3+1+1, 2+2+1, 2+1+1+1, 1+1+1+1+1+1+1
Pascal's Triangle
On the surface, a triangular shaped arrangement of numbers where a number is equal to the sum of the two numbers above it. Looking deeper, it contains many useful relations and series that are important in many branches of mathematics. The top bit looks like this:
Permutation:
a calculation where we find the number of ways to take r items from a population of n things and order them. There are a number of ways to notate this. I'll use
Triangular Numbers:
a special set of numbers that describe the number of items that can be arranged in an equilateral triangle. The list starts 1, 3, 6, 10, ... with each number being the prior number plus the next counting number (1, 1 + 2 = 3, 3 + 3 = 6, 6 + 4 = 10, etc). The nth triangular number can be found as:
Full Utilization problems can be solved using the (n-1)th Triangular Number, or
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