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?
I doubt any tutors here majored in "mason". Sorry.
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?
To determine the number of ways the seven horses can cross the finish line, we need to consider the possible positions for the tied horses.
Since two horses are tied for first place, they can finish the race in two different ways: either horse A comes first, and horse B comes second, or horse B comes first, and horse A comes second.
For the remaining five horses, there are no ties among them. Therefore, these five horses can finish the race in any order without any restrictions.
To calculate the number of ways the horses can cross the finish line, we need to multiply the number of ways for the tied horses by the number of ways for the remaining five horses.
The number of ways the tied horses can finish the race is 2 (since there are two possible orders).
The number of ways the remaining five horses can finish the race is represented by 5 factorial (5!), which is 5 × 4 × 3 × 2 × 1 = 120.
To find the total number of ways, we multiply the number of ways for the tied horses by the number of ways for the remaining horses:
Total number of ways = Number of ways for tied horses × Number of ways for remaining horses
Total number of ways = 2 × 120
Total number of ways = 240
Therefore, there are 240 different ways the seven horses can cross the finish line.
There are 7C2 = 21 ways to pick the 1st two horses, leaving 5 to arrange in the other places. So, there are
21 * 5! ways to finish the race.