# General Combination Questions

• May 16th 2010, 02:07 AM
gbooker
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?
• May 16th 2010, 06:12 AM
Soroban
Hello, gbooker!

Quote:

(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.

Quote:

(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.

• May 16th 2010, 09:47 PM
gbooker
thanks