Red, yellow, blue three-color ball each 8, take out 9, request each color ball at least one, ask how many different ways?

The corresponding parent function is:

The coefficients for which 9 corresponding combinations are taken, i.e.

Two

Chinese ellipsis is shift+^ (Chinese), or three decimal points (either in English or Mandarin).

The problem is not difficult, the error point is as follows:

1. How many methods do you ask? is not the number of permutations, then it is not necessary to multiply the inverse of factorial, i.e. x^n/n! is wrong.

2. The 2nd is the problem of calculation, unfolding is unrealistic, such as listing, my perceptual analysis is as follows, (1+X+......+X^7) ^2, the first item is 1, the last item is X^14, the largest x^7 coefficient is 8, why? I think is the method of Gaussian calculation arithmetic progression----end-to-end combination, two times the coefficients are reduced respectively, why decrement, take x^8, (x+......+x^7) The two same multiplication, then a total of 7, the coefficient is 7; X^6 is (1+x+......+x^6), so the coefficient is 6 At the end of the day, we only need the x^6 coefficients of the latter two items, then how about the ball? With the third polynomial, multiplied by the middle polynomial (the first polynomial is x^3) x^6,x^5 ... 1, then is 1*7 + 1*6+1*5+......+1*1=28.

The results are only analyzed, I asked others how we open polynomial, at the same time asked a number of polynomial multiplication how to know the coefficients of a certain item, all said I do not know, I see << combinatorial math >> Textbook discovery should be regular, ask the teacher, the teacher said you unfold, really nonsense, will not unfold ...... Did not find information, no wonder every graduate student gave him a pass or good, other teachers are excellent (class boast or praise her husband, son average 13 minutes) ...

Red, yellow, blue three-color ball each 8, take out 9, request each color ball at least one, ask how many different ways?