Question

in how many ways can 15 indistinguishable fishes be placed into 5 different ponds, so that each pond contains atleast one fish ?

Answer 1

I will use a dollar sign to represent a fish and a line as a boundary between each pond. So,

$   |   $ $   |   $ $ $   |   $ $ $ $   |   $ $ $ $ $

There are 14 slots between every two dollar signs to place a line, and we placed 4 lines.

x1 + x2 + x3 + x4 + x5 = 15

(15-1)=C4 .

14C4

14*13*12*11 / 4 * 3 * 2 * 1

24024 / 24

1,001