Answer to Question #281729 in Discrete Mathematics for Neha

Question

There are 10 stalls for animals in an exhibition. Three animals; lion, pussycat

and horse are to be exhibited. Animals of each kind are not less than 10 in

number. What is the possible number of ways of arranging the exhibition?

Answer 1

There are three types of animals and 10 stalls. One stall can be filled by any of three animals. Once the first stall is filled, the second stall can be filled again in three ways by placing any of three animals in it. We have to fill 10 such stalls and number of each animal is at lest 10, so we have

$3^{10}=59049$ ways

to fill 10 stalls.