Answer:
Permutation:
In mathematics, a permutation of a set is, loosely speaking, an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements. The word "permutation" also refers to the act or process of changing the linear order of an ordered set.
Formula:
[tex]nPr=\frac{n!}{(n-r)!}[/tex]
Example:
Permutations are the different ways in which a collection of items can be arranged. For example, the different ways in which the alphabets A, B and C can be grouped, taken all at a time, are ABC, ACB, BCA, CBA, CAB, BAC. Note that ABC and CBA are not the same as the order of arrangement is different.
Combination:
In mathematics, a combination is a selection of items from a collection, such that the order of selection does not matter.
Formula:
[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]
Example:
Combination: Picking a team of 3 people from a group of 10.
C(10,3) = 10!/(7! * 3!) = 10 * 9 * 8 / (3 * 2 * 1) = 120.
Probability:
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
Formula:
Conditional Probability P(A | B) = P(A∩B) / P(B)
Bayes Formula P(A | B) = P(B | A) ⋅ P(A) / P(B)
Example:
Probability is the likelihood or chance of an event occurring. For example, the probability of flipping a coin and its being heads is ½, because there is 1 way of getting a head and the total number of possible outcomes is 2 (a head or tail). We write P(heads) = ½.
