Question 3 Consider a team of

Question 3 Consider a team of eleven (11) soccer players, all ofwhom are equally good playersand can play any position.

(a) Suppose that the team has just finished regulation time for aplay-off game and the scoreis tied with the other team. The coach has to select five playersfor penalty kicks to decidewhich team wins the game. Since each player takes penalty kicksdifferently, the order inwhich the players are arranged for the penalty kicks is importantand can affect theoutcome. How many different ways can the coach select five (5)players to take thepenalty kicks?

(b) A couple of weeks later, the coach wants to form two (2) teamsof five (5) from theeleven players on the team for a scrimmage game (i.e., just a smallpractice game whereplayer positions are not important). The eleventh player will actas the referee. How manyways can the coach divide the team into two teams of fiveplayers?

(c) Another week later, the coach wants to test the players to beable to select a captain forthe team. Therefore, again the coach wants to form two (2) teams offive (5) from theeleven players on the team for a scrimmage game, with the eleventhplayer again actingas the referee, but with a small change. The first person chosenfor a team of five will bethe captain of the team and will have extra responsibilities. Forthe rest of the players,their roles and positions are not important. How many ways can thecoach divide theteam into two teams of five players with one captain for eachteam?




Number of ways of selecting r things out of n things is given bynCr = (n!)/{(r!)(n – r)!}……(1)

Values of nCr can be directly obtainedusing Excel Function: Math & Trig COMBIN……. (1a)

Number of ways of selecting r things out of n things when orderof selection is

important is given by: n!/(n – r)!……………………………………………………………..…. (2)

Values of n!can be directly obtained using Excel Function: Math& Trig FACT…….…. (2a)

Now to work out thesolution,

Part (a)

Vide (2),

Number of different ways the coach can select 5 players out of11 players to take thepenalty kicks, where the order in which the players are arrangedfor the penalty kicks is important

= (11!)(11 – 5)!

= 11!/6!

= 39916800/720

= 55440 Answer 1

Part (b)

Vide (1), one team of 5 players can be selected in11C5ways

another team of again 5 players can be selected out of theremaining 6 players in 16C5 ways and then theleft over player is the referee.


Number of different ways the coach can select one team of 5players, another team of again 5 players and the 11thplayer as the referee out of 11 players, where the player’spositions are not important

= (11C5) x (6C5) x1

= 462 x 6

= 2772 Answer 2

Part (c)

First player selected becomes the captain of the first team.Number of selections possible is

11C1 = 11.

Once this is done, any 4 out of the remaining 10 players canjoin the caption to form the first team.

Number of selections possible is 10C4 =210.

Now, from the remaining 6 players, first player selected becomesthe captain of the second team. Number of selections possible is6C1 = 6.

Once this is done, any 4 out of the remaining 5 players can jointhe caption to form the second team. Number of selections possibleis 5C4 = 5.

And then the left over player is the referee. Thus, the totalnumber of selections possible is:

11 x 210 x 6 x5 x 1 = 69300 Answer3


"Our Prices Start at $11.99. As Our First Client, Use Coupon Code GET15 to claim 15% Discount This Month!!"
Calculate the price
Make an order in advance and get the best price
Pages (550 words)
*Price with a welcome 15% discount applied.
Pro tip: If you want to save more money and pay the lowest price, you need to set a more extended deadline.
We know how difficult it is to be a student these days. That's why our prices are one of the most affordable on the market, and there are no hidden fees.

Instead, we offer bonuses, discounts, and free services to make your experience outstanding.
How it works
Receive a 100% original paper that will pass Turnitin from a top essay writing service
step 1
Upload your instructions
Fill out the order form and provide paper details. You can even attach screenshots or add additional instructions later. If something is not clear or missing, the writer will contact you for clarification.
Pro service tips
How to get the most out of your experience with
One writer throughout the entire course
If you like the writer, you can hire them again. Just copy & paste their ID on the order form ("Preferred Writer's ID" field). This way, your vocabulary will be uniform, and the writer will be aware of your needs.
The same paper from different writers
You can order essay or any other work from two different writers to choose the best one or give another version to a friend. This can be done through the add-on "Same paper from another writer."
Copy of sources used by the writer
Our college essay writers work with ScienceDirect and other databases. They can send you articles or materials used in PDF or through screenshots. Just tick the "Copy of sources" field on the order form.
See why 20k+ students have chosen us as their sole writing assistance provider
Check out the latest reviews and opinions submitted by real customers worldwide and make an informed decision.
Customer reviews in total
Current satisfaction rate
3 pages
Average paper length
Customers referred by a friend
15% OFF your first order
Use a coupon FIRST15 and enjoy expert help with any task at the most affordable price.
Claim my 15% OFF Order in Chat

Sometimes it is hard to do all the work on your own

Let us help you get a good grade on your paper. Get professional help and free up your time for more important courses. Let us handle your;

  • Dissertations and Thesis
  • Essays
  • All Assignments

  • Research papers
  • Terms Papers
  • Online Classes