Q4Choosing a lineup for a traveling basketball team There ar

Q#4Choosing a lineup for a traveling basketball team.

There are 20 members of a basketball team.

(a) The coach must select 12 players to travel to an away game. How many ways are there to select the players who will travel?

(b) From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. How many ways are there for her to select the starting line-up?

(c) From the 12 players who will travel, the coach must select her starting line-up. She will select a player for each of the five positions: center, right forward, left forward, right guard, left guard. However, there are only three of the 12 players who can play center. Otherwise, there are no restrictions. How many ways are there for her to select the starting line-up?

Solution

a)

C(20,12)

b)

The number of ways is P(12,5) ie number of ways of permuting 12 objects in a string of length 5

c)

So we first select the centre first

in C(3,1)=3 ways

Now we have 11 players and 4 positions

SO, P(11,4) for remaining positions

So, 3P(11,4)