Combinatorics-Kenneth Rosen(Ex 5.3-41)

Question

How many ways are there for a horse race with three horses to finish if ties are possible.(Two or three horses may tie).

Answer 1

P, Q,  R are horses and 1-3 are the positions :
(a) 1 2 3 - > 3! = 6 ways
(b) 1 2 2- > 3!/2! = 3 ways
(c) 1 1 2 -> 3!/2! = 3 ways
(d) 1 1 1 -> 1 way

Total ways = 6+3+3+1 = 13 ways.