Specialist Maths - Unit 1 Topic 1 - Combinatorics Flashcards

Flashcards on Combinatorics, including set notation, multiplication and addition principles, permutations, factorials and combinations.

Use the __ principle.

Formulas to determine the number of elements in the union of two and the union of three sets.

A __ (S)

Is a collection of objects. The objects in a set are the ‘elements’ of the set. Denoted by {} or [].

The __ of S, written as S′

Is the set of all things NOT in S.

The __ of S and T

Is all the elements in either S or T or both.

In general, for two sets S and T, the size of the union of these sets is:

n(S∪T)=n(S)+n(T)−n(S∩T).

__ techniques allow us to determine the number of ways an activity can occur.

Counting techniques allow us to determine the number of ways an activity can occur and calculate the probability of an event.

When order is important, this is called an or a

When order is important, this is called an arrangement or a permutation; when it is not important, it is called a selection or a combination.

Using the __ principle should be used when there are events (A and B), where one event is followed by another

Should be used when there are events (A and B), where one event is followed by another (when order is important).

__ principle Should be used when two distinct operations or events occur in which one event is not followed by another

Should be used when two distinct operations or events occur in which one event is not followed by another — that is, when the events are mutually exclusive.

n!

Multiplying each of the integers from n down to 1

__ is often used instead of the term ‘arrangement’

Is often used instead of the term ‘arrangement’

When letters are repeated, the number of different arrangements will be __

When letters are repeated, the number of different arrangements will be reduced compared to the number of arrangements produced if the letters were all different.

__ When order does not matter

When order does not matter