回複：回複：請教解數學題。

f($n,1) should be 1, which is a typo above.

We can see the formula after a few steps. Here is the trick.
f($n,1)=(n+1-1) choose 0 = 1
f($n,2)=(n+2-1) choose 1= n+1
f($n,3)=(n+3-1) choose 2 = (n+2)(n+1)/2
f($n,4)=(n+4-1) choose 3 = (n+3)(n+2)(n+1)/6

The answer to your second question should be (20)(19)(18)(17)(16)/24.

Am I wrong?

所有跟帖： 

• 回複：回複：回複：請教解數學題。 -guest1000- ♂ (45 bytes) () 09/07/2010 postreply 19:51:53

• 第二題答案是不是:C(16+3,3)+C(15+3,3)+...+C(1+3,3)+C(0+3,3) -皆兄弟也- ♂ (0 bytes) () 09/08/2010 postreply 09:10:55

• I think we should change 16 to 20....we get C(24,4)=... -jinjing- ♀ (0 bytes) () 09/08/2010 postreply 09:35:30

• how to understand: must be invested among 4 possible opportuniti -皆兄弟也- ♂ (81 bytes) () 09/08/2010 postreply 10:00:33

• even if we should change 16 to 20....we get C(21,4)=... -皆兄弟也- ♂ (0 bytes) () 09/08/2010 postreply 10:03:46

• sorry, C(21,4)=... wrong; C(24,4)=... right,if we should change -皆兄弟也- ♂ (0 bytes) () 09/08/2010 postreply 10:07:18

• you are right:C(20,4)=C(16+3,3)+C(15+3,3)+...+C(1+3,3)+C(0+3,3) -皆兄弟也- ♂ (0 bytes) () 09/08/2010 postreply 10:09:50

• 第二題:What if not all money need be invested? 可這樣理解： -皆兄弟也- ♂ (271 bytes) () 09/08/2010 postreply 10:37:04

• 我認為，您的第一題答案是正確的。 -皆兄弟也- ♂ (265 bytes) () 09/08/2010 postreply 09:03:17

• 回複：我認為，您的第一題答案是正確的。 -guest1000- ♂ (327 bytes) () 09/08/2010 postreply 12:31:24

• yes,您的第二題答案是正確的,as well。 -皆兄弟也- ♂ (0 bytes) () 09/08/2010 postreply 13:03:14

• Put 16 balls in 5 bins, no matter 5 bins can be empty or not, wh -皆兄弟也- ♂ (0 bytes) () 09/08/2010 postreply 13:17:31