probability

[mehrasa]

on a 5-5 soccer game, all 5 players scored 6 goals. in how many ways we can distribute 6 goals between 5 players?

Answer: we can use this formula
when we have n identical thing to distribute among r people : n+r-1Cr-1
==> 10C4= 210

look at this Q
there are 4 contestant with 6 prizes... in how many ways these 4 contestant win prizes?

OA is 6*5*4*3 =360

MY Q is that why we can not use the above formula for the second Q? what is the difference?

[mehrasa]

can anybody help?

[shankar.ashwin]

I am not sure about the first question, could you post the exact wording of it. But one difference is goals are not distinct whereas prizes are

In the second question you have 6 different prices (earlier problems goals cannot be distinct, so it would become a combination problem).

Now say you have 4 positions 1st,2nd, 3rd and 4th.

the 1st position winner can get any of the 6 gifts - 6 possibilities.
the 2nd can get any of the 5 from remaining - 5 possibilities.

Similarly for 4 positions we have 6*5*4*3 = 360.