1. ## General Combination Questions

just some questions that i need help with, if someone could help, it would be appreciated very much

q1. find the number of ways of arranging 7 people in a line with the tallest in the middle

q2. a squad of footballers has 10 midfielders, 3 goalkeepers and 7 defenders. how many teams (of 11 players) could be selected if the team only has one goalkeeper and at least 5 midfielders and at least 4 defenders?

2. Hello, gbooker!

(1) Find the number of ways of arranging 7 people in a line
with the tallest in the middle.

Place the lallest in the middle.

Then the other six people can be arranged in $\displaystyle 6! = 720$ ways.

(2) A squad of footballers has 3 Goalkeepers, 10 Midfielders, and 7 Defenders.
How many teams (of 11 players) could be selected if the team has:
one Goalkeeper and at least 5 Midfielders and at least 4 Defenders?
There are two possible team compositions:

. . $\displaystyle 1G,\;6M,\;4D\!:\;\;{3\choose1}{10\choose6}{7\choos e4} \;=\;22,\!050$ possible teams.

. . $\displaystyle 1G,\;5M,\;5D\!:\;\;{3\choose1}{10\choose5}{7\choos e5} \;=\;15,\!876$ possible teams.

Therefore, there are: .$\displaystyle 22,\!050 + 15,\!876\;=\;37,\!926$ possible teams.

3. thanks