A team of 3 students is to be formed from a class of 25 students.

How many ways are there to form this team if there is 1 team leader, 1 scribe and 1 timekeeper in the team? Each person can only perform one role at a time.

Question

A team of 3 students is to be formed from a class of 25 students. 

How many ways are there to form this team if there is 1 team leader, 1 scribe and 1 timekeeper in the team? Each person can only perform one role at a time.

anonymous · Answer

$$\large _{25}P_{3}=\frac{25!}{(25-3)!}=25\times24\times23$$

anonymous · Answer

Oh thanks, I got 2300 which was wrong...

anonymous · Answer

You used $\large _{25}C_3$ which doesn't take order into account.

If you were to list all the possible arrangements, $\large _{25}P_3$ counts all of them, i.e.
123
132
213
231
312
321

whereas $\large _{25}C_3$ does not consider the order, i.e.
123

anonymous · Answer

Thanks for the good explanation ^^