There are seven ice skaters in a competition. How many different possibilities are there for the top three places? (A different ordering of the same three skaters counts as a different possibility.

Question

anonymous · Answer

$$7*3=21$$

kropot72 · Answer

There are 7 possibilities for first place. For each of the 7 possibilities for first place there are 6 possibilities for second place and for each of the 7 * 6 possibilities for first and second place there are 5 possibilities for third place.
Therefore the total number of possibilities for the top three places is found from
$$7\times 6\times 5$$