1.
Welcome to Combinations WEEK!
4. A sequence of numbers or letters used to open a combination.

2. 5. Mathematics One or more elements selected from a set without regard to the order of selection.
Combination Formula
A formula for the number of possible
combinations of r objects from a set of n
objects. This is written in any of the ways shown
below.
All forms are read aloud "n choose r."
Forml
a:
Note:
, where nPr is the
formula for permutations of n objects
taken r at a time.

3. Examl
e:
How many different committees of 4
students can be chosen from a group
of 15?
Answe
r:
There are
possible combinations
of 4 students from a set of 15.
Permutation and Combination
Principle
There are 1365 different committees.
The number of ways of picking
unordered outcomes from
coefficient or choice number and read "
choose ,"
possibilities. Also known as the binomial

4. where
is a factorial (Uspensky 1937, p. 18). For example, there are
elements out of the set
, namely
These combinations are known as k­subsets.
The number of combinations
,
,
combinations of two
,
,
, and
.
can be computed in Mathematica using Binomial[n, k], and the combinations
themselves can be enumerated in Mathematica using Subsets[Range[n], k ].
Muir (1960, p. 7) uses the non standard notations
and
.