Ten high school students on student council are now eligible to run for the positions of president, vice president, and secretary. How many unique permutations of these 10 students filling the 3 positions are possible?

Question

anonymous · Answer

so if theres 10 students and 3 spots wouldnt you just multiplty to see how many different possibilites there are? idk. i know its not that simple

unicornpoopcookies · Answer

= 10 * 9 * 8
= 720

Answer: 720 possibilities

anonymous · Answer

why would you multiply it by 9 though?

anonymous · Answer

$$
10P7 = \frac{10!}{7!} = \frac{10\times9\times8\times7!}{7!} = 10\times 9\times 8
$$