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For an 8-a-side football match, a coach has to choose
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07 Dec 2018, 22:44
07 Dec 2018, 22:44
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Question Stats:
48% (02:15) correct
51% (02:39) wrong based on 39 sessions
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For an 8-a-side football match, a coach has to choose the team from a squad of 12 boys. Only three of them can play as a goalkeeper and these three cannot play any other position. The other boys can play all the other positions - defense, midfield and forward. If the team should have 1 goal keeper, 3 defenders, 3 midfielders and 1 forward, in how many ways can the coach select the team?
a. 495
b. 108
c. 544320
d. 12580
e. 15120
a. 495
b. 108
c. 544320
d. 12580
e. 15120
Re: For an 8-a-side football match, a coach has to choose
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08 Dec 2018, 02:31
08 Dec 2018, 02:31
Expert Reply
Please, post the question under the right sub-forum.
Moreover, follow the rules https://gre.myprepclub.com/forum/rules-for ... -1083.html
Thank you for your collaboration.
Regards
Moreover, follow the rules https://gre.myprepclub.com/forum/rules-for ... -1083.html
Thank you for your collaboration.
Regards
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For an 8-a-side football match, a coach has to choose
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16 Aug 2019, 05:46
16 Aug 2019, 05:46
Roy5522 wrote:
For an 8-a-side football match, a coach has to choose the team from a squad of 12 boys. Only three of them can play as a goalkeeper and these three cannot play any other position. The other boys can play all the other positions - defense, midfield and forward. If the team should have 1 goal keeper, 3 defenders, 3 midfielders and 1 forward, in how many ways can the coach select the team?
a. 495
b. 108
c. 544320
d. 12580
e. 15120
a. 495
b. 108
c. 544320
d. 12580
e. 15120
Take the task of creating the team and break it into stages.
We’ll begin with the most restrictive stage.
Stage 1: Select a boy to be goalkeeper
We can choose any of the 3 boys who can only be goalkeeper, so we can complete stage 1 in 3 ways
Stage 2: Select 3 defenders
There are 9 boys who can play any non-goaltender position
Since the order in which we select the 3 defenders does not matter, we can use combinations.
We can select 3 boys from 9 boys in 9C3 ways (84 ways)
So, we can complete this stage 84 ways
Stage 3: Select 3 midfielders
Since we already selected 3 of the 9 boys in stage 2, there are now 6 boys remaining
Since the order in which we select the 3 midfielders does not matter, we can use combinations.
We can select 3 boys from 6 boys in 6C3 ways (20 ways)
So, we can complete this stage 20 ways
Stage 4: Select 1 forward
There are now 3 boys remaining
So, we can select 1 forward in 3 ways
By the Fundamental Counting Principle (FCP), we can complete all 4 stages (and thus create an 8-person team) in (3)(84)(20)(3) ways (= 15,120 ways)
Answer: E
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
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