Question

there are 1320 ways for three students to win first,second,and third place during a debate match.how many students are there on the debate team? explain your reasoning.

Answer 1

There are 12 students on the team.

The number of permutations of n objects taken r at a time is given by
$_nP_r= \frac{n!}{(n-r)!}$

Since factorials are numbers multiplied by the number below them, down to 1, we know that the entire problem is multiplication.  Since 1320 ends in 0, we know that it is divisible by 10, so there is a good chance 10 is one of the factors.  

1320/10 = 132

From our multiplication tables, we know that 132=12*11; this means that we have 12*11*10 = 1320.  Since 12 is the largest factor, we know that there are 12 students on the team.