Seven contestants made it to the semifinals of the Miss Rainstorm Pageant. Awards will be given to the third runner up, the second runner up, the first runner up, and the winner of the pageant will be crowned Miss Rainstorm. How many different ways can the three runners up and the winner be chosen? 35

Question

Seven contestants made it to the semifinals of the Miss Rainstorm Pageant. Awards will be given to the third runner up, the second runner up, the first runner up, and the winner of the pageant will be crowned Miss Rainstorm. How many different ways can the three runners up and the winner be chosen? 35<<>>>>>

anonymous · Answer

How many options for first place?
One first place is chosen, how many options for second place?
Once first and second are chosen, how many options for third?

anonymous · Answer

Oh crap. I'm sorry

anonymous · Answer

This is different from $$\left(\begin{matrix}7 \ 4\end{matrix}\right)$$

anonymous · Answer

Not even thinking.

anonymous · Answer

It's okay. It's a permutation, not a combination.

anonymous · Answer

Subtle difference.

anonymous · Answer

knowing the first second 3rd what you add them together ?

anonymous · Answer

No, you multiply them; we have 7 choices for first place, 6 for second place, 5 for third and 4 for fourth.  So the total number is 7*6*5*4 = 840

anonymous · Answer

ok thanks