It is a bit difficult for junior high school students to do this. C and a are the knowledge of permutation and combination. Simply put, from n different elements, any M (M ≤ N, m and n are natural numbers, the same below) elements are arranged in a column in a certain order, which is called the arrangement of m elements in n different elements; All permutation numbers of m(m≤n) elements from n different elements are called permutation numbers of m elements from n different elements, which are represented by symbols.

A(n, m) means. Arrangement: a (n, m) = n (n-1) (n-2) ... (n-m+1) = n! /(n-m)！ ; Where n! =n*(n- 1)*(n-2).....* 1，(n-r)！ =(n-m)*(n-m- 1)...*2* 1。

. (m≤n)

Combination: take any r(r≤n) elements from n different elements and group them, which is called the combination of taking r elements from n different elements; All combination numbers of r(r≤n) elements taken from n different elements are called combination numbers of r elements taken from n different elements. Use symbols

C(n, r) represents. C(n，r)=A(n，r)/r！ ,

. There is an order in the arrangement, but there is no order in the combination. Arrangement can be regarded as combining first and then arranging in order.

(x+y) n and (x-y) n can be solved by binomial theorem.

, where σ is the sign of summation.

Formula features: (1) Formula * * has n+ 1

(2) The binomial coefficients are c (n, 0), c (n, 1),,, and C(n, n).

(3) General formula (general term): c (n, r) * a (n-r) * b r,,, r = (0, 1, 2,3, ... n- 1).

(4) Exponent: The exponent of A decreases from n to 0, and the exponent of B increases from 0 to n. 。