Question

12 different objecs are to be distributed among 9 persons. Find the number of ways in which objects can be distributed . (All objects must be distributed and each person should get atleast 1 object)

Answer 1

No. of ways of distributing $12$ objects among $9$ persons to that each gets atleast one

$=C_{9-1}^{12+9-1}=C_8^{20}=\frac{20!}{8!\times 12!}=\frac{20\times 19\times 18\times 17\times 16\times 15\times 14\times 13\times 12!}{8\times 7\times 6\times 5\times 4\times 3\times 2\times 12!}=19\times 17\times 15\times 13\times 2$

$=125970$ways