數學難題,,幫幫手PLZ~

Q: w, x, y, z 為正整數, w ＋ x ＋ y ＋ z ＝ 20. w, x, y, z 最多有幾多個組合?

Sol:

I have to remind you, 0 is not positive integer.

therefore, w, x, y, z ≧ 1

H(4,16) ＝ C(19,3)

＝ ( 19 * 18 * 17 ) / ( 3 * 2 * 1 )

＝ 5814 / 6

＝ 969

Ans: 969 個

P.S I think you question should be w, x, y, z are non-negative integer.

therefore, w, x, y, z ≧ 0

H(4,20) ＝ C(23,3)

＝ ( 23 * 22 * 21 ) / ( 3 * 2 * 1 )

＝ 10626 / 6

＝ 1771

The answer will become 1771.

If any step you don’t understand, send me a letter.

w,x,y,z最多有無限個組合
因為w,x,y,z可能係小數