Question

Seven horses are entered in a race. If five horses are tied for first place, and there are no ties among the other two

horses, in how many ways can the seven horses cross the finish line

Answer 1

Explanation:

the way I understand it, this means in how many ways can we pick 2 of the 7 horses, when the sequence of these 2 horses matters, but the sequence of the remaining 5 horses does not matter (as they finishing tied or not even starting is in that sense the same thing).

so, we are looking for the permutations of 2 out of 7 elements.

that is

7! / (7-2)! = 7×6 = 42

there are 42 different ways for these 7 horses to cross the finish line in the described constellation.