Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Coach Miller is filling out the starting lineup for his [#permalink]

Show Tags

17 Jan 2005, 13:40

This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Coach Miller is filling out the starting lineup for his indoor soccer team. There are 10 boys on the team, and he must assign 6 starters to the following positions: 1 goalkeeper, 2 on defense, 2 in midfield, and 1 forward. Only 2 of the boys can play goalkeeper, and they cannot play any other positions. The other boys can each play any of the other positions. How many different groupings are possible?

It is not clear to me how order of picking 2 on defense, 2 in midfield etc matters, for me it was just number of ways for creating a team by picking 1 goalkeeper out of 2 i.e. 2C1 way and rest of 5 members from 8 ppl, in 8C5. Total of 112 ways

2c1*8c2*6c2*4c1
but taking like this my question is how are we distinguishing between the goal keepers and the rest in the sense.. the 2 eligible goal keepers cannot play the other positions where as allt he other can..

When you consider the first choice 2C1 to select the goalkeepers then you put then out of the pool in filling the next position in 8C2 ways. We do not care wo they really are, just that 2 of them are allocated to this job and then are not part of the remaining players choice.

It is not clear to me how order of picking 2 on defense, 2 in midfield etc matters, for me it was just number of ways for creating a team by picking 1 goalkeeper out of 2 i.e. 2C1 way and rest of 5 members from 8 ppl, in 8C5. Total of 112 ways

banerjeea_98, you are OK so far, but you have not finished: you need to arrange those 5 you pick for the team in their categories: 5C3 * 3C2 *1C1.

So total 2C1 * 8C5 * 5C2 * 3C2 1*1 = 112 * 30 = 3360

When you consider the first choice 2C1 to select the goalkeepers then you put then out of the pool in filling the next position in 8C2 ways. We do not care wo they really are, just that 2 of them are allocated to this job and then are not part of the remaining players choice.