seven horses are entered in a race. If two horses are tied for first​ place, and there are no ties among the other five ​horses, in how many ways can the seven horses cross the finish​ line?

Answer 1

So first you want to know how many pairs I can form from the 7 horses , then arranging the other 5
That would be C(7,2) or 21 for the first part
- the remaining 5 horses can be arranged in
5! or 120 ways

So there are 21(120) or 2520 ways to finish the race

Answer 2

Old MacDonald had some horses, cows, and pigs, on his farm. He had 69 water troughs from which these animals drink. Horses drank only from the horse troughs, exactly two horses for each trough. Cows drank from cow troughs, exactly three cows per trough and pigs drank from pig troughs, exactly eight pigs per trough. Old MacDonald’s farm has the same number of horses, cows, and pigs. How many animals does Old MacDonald have on his farm?