If ten 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)720
B)90
C)6
D)7,920
E)5,040

Question

Quizplus · Accepted Answer

The number of different ways to decide first, second, and third place among ten teams, without allowing ties, can be calculated using permutations. This is because the order in which the teams are placed matters. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of items (in this case, teams) and r is the number of items to be arranged. Here, n = 10 (teams) and r = 3 (places to be decided). Thus, the calculation is 10P3 = 10! / (10 - 3)! = 10! / 7! = (10 × 9 × 8 × 7!) / 7! = 720.

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