If eleven basketball teams are in a tournament, find the number of different ways that first, second, and third place can be decided, assuming ties are not allowed.
A)110
B)6
C)7,920
D)11,880
E)990

Question

Quizplus · Accepted Answer

The number of different ways to decide first, second, and third place among eleven teams, assuming no ties, is calculated using permutations since the order matters. The formula for permutations is $nPr = \frac{n!}{(n-r)!}$, where $n$ is the total number of items, and $r$ is the number of items to choose. Here, $n = 11$ (teams) and $r = 3$ (places). Thus, the calculation is $11P3 = \frac{11!}{(11-3)!} = \frac{11!}{8!} = 11 \times 10 \times 9 = 990$.

If Eleven Basketball Teams Are in a Tournament, Find the Number