The number of all combinations of m(m≤n) elements from n different elements is called the number of combinations of m elements from n different elements. It is represented by the symbol c(n, m). c(n，m)=p(n，m)/m！ =n！ /((n-m)！ *m！ )。

This is all the combinations of four out of six * * * There are six in all! /((6-4)! *4! ) = 6 * 5 * 4 * 3 * 2 *1/2 *1* 4 * 3 * 2 *1= 15, so * * has15 groups.

Extended data:

The development of permutation and combination:

In 1772, the French mathematician Vandermonde, (A.-T.) used [n]p to express the number of permutations in which p is taken from n different elements at a time.

Euler (L.), a Swiss mathematician, used 177 1 and 1778 to represent the combination number of p elements of n different elements.

1830, the British mathematician peacock (g) introduced the symbol Cr to represent the number of r in a combination of n elements.

1869 or earlier, Goodwin of Cambridge used the symbol nPr to indicate the arrangement number of R elements taken out of N elements at a time, and this usage has continued to this day. According to this method, nPn is equivalent to n! .

1872, German mathematician B. A. von introduced the symbol (np) to express the same meaning, and this combination of symbols (combined symbols) has been used to this day.

In 1880, Potts (R R.) indicates the number of combinations and permutations of R from n elements by nCr and nPr respectively.

The calculation method of permutation and combination is as follows:

The arrangement a (n, m) = n× (n- 1). (n-m+ 1) = n！ /(n-m)！ (n is subscript and m is superscript, the same below)

Combination C(n, m)=P(n, m)/P(m, m) =n! /m！ (n-m)！ ;

For example:

A(4，2)=4！ /2! =4*3= 12

C(4，2)=4！ /(2! *2! )=4*3/(2* 1)=6