Adrienne, Heather, Katie, Sara and Kara ran a race. At the end of the race, two of the friends finished in a tie while the rest all finished in different times. In how many possible orders could the girls have finished the race?

Consider the two who tied as a single person. Then there would be 4! ways to finish. But there are 5C2=10 ways to pick the two girls, so there are

4!*10 = 240 ways to finish.

Well, that's quite a race! Let me see if I can count the possibilities while cracking a joke or two along the way.

We know that two friends finished in a tie, so let's start with those two and call them Tie Twins. Adrienne, Heather, Katie, Sara, and Kara are probably giving them some friendly side-eye.

Now, for the Tie Twins, we have two possibilities: either the first twin finished before the second twin or vice versa.

So, we have 2 possibilities for the Tie Twins. As for the other three friends, let's arrange them separately, one by one.

We have three remaining spots to fill, and three friends to choose from: Adrienne, Heather, and Katie. So we have 3! (3 factorial) possibilities for them.

Now, let's multiply all the possibilities together: 2 x 3! = 2 x 3 x 2 x 1 = 12.

So, in total, there are 12 possible orders in which Adrienne, Heather, Katie, Sara, and Kara could have finished the race.

I hope that answer made you race with laughter!

To find the number of possible orders in which the girls could have finished the race, we need to consider the number of ways we can arrange them.

Since two friends finished in a tie and the rest finished in different times, we can consider these two friends as a single entity. Let's call this entity "Tie".

So, we have 4 entities - Adrienne, Heather, Katie, and Sara (Kara is already included in the "Tie" entity).

The number of ways to arrange these entities can be calculated using the factorial function (n!):
4! = 4 x 3 x 2 x 1 = 24

Therefore, there are 24 possible orders in which the girls could have finished the race.

To determine the number of possible orders in which the girls could have finished the race, we can use the concept of permutations.

First, let's consider the two friends who finished in a tie. There are 2 ways to arrange these two friends since they finished at the same time.

Now, we have 3 friends left who finished in different times. There are 3! (read as "3 factorial") ways to arrange these three friends, which means 3 × 2 × 1 = 6 possible orders.

To find the total number of possible orders, we multiply the number of ways to arrange the tied friends (2) by the number of ways to arrange the remaining friends (6). Thus, the total number of possible orders is 2 × 6 = 12.

Therefore, there are 12 possible orders in which the girls could have finished the race.