There are 15 teams in the Eastern conference of the national

There are 15 teams in the Eastern conference of the national hockey league for the 2009-2010 season, divided into 3 divisions of 5 teams each. Eight of these teams will participate in the playoffs. The division winner from each division goes to the playoffs; in addition, the next 5 ranked teams in the conference, based on regular season records, will participate in the playoffs. How many different collections of eight teams from the eastern conference could go to the playoffs?

Solution

The winner from the first division can be selected in 5C1 ways (1 winner is selected from 5 people), the winner from the second division can be selected in 5C1 ways and the winner from the third division can be selected in 5C1 ways

Number of ways = 5C1 * 5C1 * 5C1 = 125 ways

Remaining 12 teams are there , 5 teams are to be selected

=> 12C5 = 12!(7!5!) = (12 * 11 * 10 * 9 * 8)/120 = 792

Total Number of ways = 125 + 792 = 917 ways