Wikipedia: Combinations

Difference (from prior author revision) (major diff, minor diff)

Changed: 1,2c1,4

Let S be a set. The combinations of this set are its subset. A k-combination
is a subset of with k elements.

Combinations are studied in combinatorics: let S be a set; the combinations of this set are its subsets. A k-combination
is a subset of S with k elements.
The order of listing the elements is not important in combinations: two lists with the same elements in different orders are considered to be the same combination.
The number of k-combinations of set with n elements is the binomial coefficient "n choose k", written as C(n, k).

Changed: 4c6,11

The order of listing of elements in these subsets is not important in combinations, two lists with the same elements in different orders are considered the same combination.

One method of determining a formula for C(n, k) proceeds as follows:
#We count the number of ways in which we can make a list of k different elements from the set of n. This is equivalent to calculating the number of k-permutations.
#Recognizing that we have listed every subset many times, we correct the calculation by dividing by the number of different lists containing the same k elements:
:C(n, k) = P(n, k) / P(k, k)
Since P(n, k) = n! / (n-k)! (see factorial), we find
:C(n, k) = n! / (k! * (n-k)!)

Changed: 6,14c13

The number of k-combinations of set of n elements if the binomial number 'n over k'.

One method of counting combinations of k elements from a set of n elements proceeds as follows:
#We count the number of ways in which we can make a list of k elements from the set of n. This is equivalent to calculating the number of Permutations.
#Recognizing that we have listed every subset many times, we correct the calculation by dividing by the number of different lists containing the same k elements.
*_nC_k = _nP_k / _kP_k
Since _nP_k = n!/(n-k)!, we find
*_nC_k = n!/(k!*(n-k)!)
It is useful to note that _nC_k can be found using the [Pascal Triangle]?.

It is useful to note that C(n, k) can also be found using the Pascal triangle, as explained in the binomial coefficient article.

Combinations are studied in combinatorics: let S be a set; the combinations of this set are its subsets. A k-combination is a subset of S with k elements. The order of listing the elements is not important in combinations: two lists with the same elements in different orders are considered to be the same combination. The number of k-combinations of set with n elements is the binomial coefficient "n choose k", written as C(n, k).

One method of determining a formula for C(n, k) proceeds as follows:

We count the number of ways in which we can make a list of k different elements from the set of n. This is equivalent to calculating the number of k-permutations.
Recognizing that we have listed every subset many times, we correct the calculation by dividing by the number of different lists containing the same k elements:

: C(n, k) = P(n, k) / P(k, k)

Since P(n, k) = n! / (n-k)! (see factorial), we find

: C(n, k) = n! / (k! * (n-k)!)

It is useful to note that C(n, k) can also be found using the Pascal triangle, as explained in the binomial coefficient article.