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 find the number of ways the horses can cross the finish line, we can count the possibilities for each position one by one.
First, let's consider the two horses tied for first place. Since there are two possibilities for the top spot, we can place them in the first position in 2 ways.
Now, we have 5 remaining horses left to arrange.
The second position can be filled by any one of the remaining 5 horses, so there are 5 choices for the second position.
Similarly, for the third position, there are 4 remaining horses to choose from.
For the fourth position, there are 3 remaining horses, and for the fifth position, there are 2 remaining horses.
Finally, there is only 1 horse left to be placed in the sixth position.
Therefore, the total number of ways the horses can cross the finish line is given by multiplying the number of choices for each position:
2 * 5 * 4 * 3 * 2 * 1 = 240
So, there are 240 ways in which the seven horses can cross the finish line.