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# A team of 3 students is to be selected out of 4 study groups

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Director
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A team of 3 students is to be selected out of 4 study groups  [#permalink]

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25 Dec 2018, 15:12
1
00:00

Difficulty:

35% (medium)

Question Stats:

69% (00:57) correct 31% (01:29) wrong based on 42 sessions

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A team of 3 students is to be selected out of 4 study groups, each study group containing 4 students. What is the number of different teams that can be selected if more than one student cannot be selected from a study group?

A) 24

B) 256

C) 536

D) 544

E) 1536

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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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25 Dec 2018, 19:40
3 teams can be selected from 4 in 4C3 ways= 4 ways
now 1 member can be selected from a group of 4 is 4C1=4 ways & 3 members to be selected 1 from each 3 selected groups.
Hence total number of ways = (4C1*4C1*4C1)*4C3=4*4*4*4=256 .... Hence Ans B
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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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25 Dec 2018, 22:16
You need to select three groups to select one student each.
One student from each group can be selected in 4 different ways.
And three groups out of 4 can be selected in 4c3 = 4 different ways.
Multiplying both together = 4*4*4*4 = 256

definitely not a 700 level question
Director
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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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26 Dec 2018, 03:35
ruchik wrote:
You need to select three groups to select one student each.
One student from each group can be selected in 4 different ways.
And three groups out of 4 can be selected in 4c3 = 4 different ways.
Multiplying both together = 4*4*4*4 = 256

definitely not a 700 level question

I agree with you, though, I got it from e-mat test, and it was categorized as "hard" question.
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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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28 Dec 2018, 01:14
ruchik wrote:
You need to select three groups to select one student each.
One student from each group can be selected in 4 different ways.
And three groups out of 4 can be selected in 4c3 = 4 different ways.
Multiplying both together = 4*4*4*4 = 256

definitely not a 700 level question

Hey,
I have question. If order doesn't matter over here then why aren't we dividing it.
Director
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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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28 Dec 2018, 01:50
1
ashu2107 wrote:
Hey,
I have question. If order doesn't matter over here then why aren't we dividing it.

greetings ashu2107

The objective of the problem consists of 2 tasks:

Task 1) Select the 3 study groups (out of the total 4) that will contribute 1 student each to the Team.
Task 2) Within each study group selected in Task 1, select 1 (out of the total 4) students who will go into the Team.

Since both these tasks need to be done to fulfill the objective, the Principle of Multiplication will apply:
(Number of ways to select a team as specified) = (Number of ways to do Task 1)*(Number of ways to do Task 2)

Number of ways to do Task 1 = 4C3=4

Let’s consider one out of the 3 study groups selected in Task 1:
1 out of the 4 students in this study group has to be selected for the Team. This can be done in 4C1 = 4 ways

Similarly, in the second selected study group also, the number of ways to select 1 student out of the 4 students will be equal to 4. Same will be the case for the third study group as well.
So, number of ways to do Task 2 = 4*4*4 = 64

Therefore, (Number of ways to select a team as specified) = 4*64 = 256
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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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28 Dec 2018, 05:02
Mahmoudfawzy83 wrote:
A team of 3 students is to be selected out of 4 study groups, each study group containing 4 students. What is the number of different teams that can be selected if more than one student cannot be selected from a study group?

A) 24

B) 256

C) 536

D) 544

E) 1536

There are 4 students groups and 3 students to be selected from these groups with a condition that not more than one student can be selected from each group.

So, lets first select the 3 groups out of 4. This can be done is 4C3 ways = 4 ways

Now 1 student from each group can be selected in 4*4*4 = 64 ways.

So, total number of ways = 64 * 4 = 256 ways.

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Re: A team of 3 students is to be selected out of 4 study groups  [#permalink]

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28 Dec 2018, 09:53
ashu2107 wrote:
Hey,
I have question. If order doesn't matter over here then why aren't we dividing it.

Given that there are 16 students divided into 4 different groups of 4 each.

Required is to form a group of 3 students, with not more than one student from one group.

First student can be selected in 16 ways, second student can be selected in 12 ways and the third student can be selected in 8 ways. Since the order doesn't matter, we get

# of ways to form the group of 3 = (16 * 12 * 8)/3! = 256 ways

Thanks,
GyM
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Re: A team of 3 students is to be selected out of 4 study groups   [#permalink] 28 Dec 2018, 09:53
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