Question

I coach a soccer team with 15 members. i want to choose a starting lineup consisting of 11 players, two of whom will represent the team in the captains meeting at the beginning of the game. in how many ways can i choose my starting lineup, including designating the two captains?

Answer 1

`{_(15)C_(11)}\cdot {_(11)C_2}=(15!)/(11!4!)\cdot(11!)/(2!9!)=(12\cdot13\cdot14\cdot15)/(2\cdot3\cdot4)\cdot(10\cdot11)/(2)=75,075`

Answer 2

Answer: There are 715 ways to choose his starting lineup which includes designating the two captions.

Explanation:

Since we have given that

Number of members = 15

Number of players = 11

Number of captions must be included = 2

So, Number of remaining members = 15-2 = 13

Number of remaining players = 11 - 2 = 9

So, Number of ways to choose starting line up is given by

`^(13)C_9\\\\=715`

Hence, there are 715 ways to choose his starting lineup which includes designating the two captions.