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How many different groups of 3 people can be formed from a group of 5

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niheil
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How many different groups of 3 people can be formed from a group of 5 [#permalink] New post   Updated on: 13 Mar 2019, 05:11
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How many different groups of 3 people can be formed from a group of 5 people?

A. 5
B. 6
C. 8
D. 9
E. 10
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E

Originally posted by niheil on 10 Oct 2010, 14:19.
Last edited by Bunuel on 13 Mar 2019, 05:11, edited 1 time in total.
Renamed the topic.
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Re: How many different groups of 3 people can be formed from a group of 5 [#permalink] New post   10 Oct 2010, 14:23
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niheil wrote:
Does anyone think there's a faster way to solve this problem:

How many different groups of 3 people can be formed from a group of 5 people?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10


How I solved the problem
Show Spoiler
I solved the problem by listing all the possible combinations (123, 124, 125...). But I have a feeling there's a shortcut to solving this problem.



Addition info on the problem
Source: Paper Test
Test Code 42
Section 4
Problem 14


The number of ways to choose r objects out of n objects is \(C(n,r)=\frac{n!}{r!(n-r)!}\)

Using this formula, the answer is C(5,3) or 10.
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Re: How many different groups of 3 people can be formed from a group of 5 [#permalink] New post   10 Oct 2010, 14:25
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Expert Reply
niheil wrote:
Does anyone think there's a faster way to solve this problem:

How many different groups of 3 people can be formed from a group of 5 people?
(A) 5
(B) 6
(C) 8
(D) 9
(E) 10


How I solved the problem
Show Spoiler
I solved the problem by listing all the possible combinations (123, 124, 125...). But I have a feeling there's a shortcut to solving this problem.



Addition info on the problem
Source: Paper Test
Test Code 42
Section 4
Problem 14


Choosing 3 distinct objects out of 5 when order of the selection is not important \(C^3_5=\frac{5!}{3!(5-3)!}=10\).

Answer: E.

Check Combination topic of Math Book: math-combinatorics-87345.html

Hope it helps.
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niheil
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Re: How many different groups of 3 people can be formed from a group of 5 [#permalink] New post   10 Oct 2010, 22:12
Thanks shrouded1 and Bunuel! Your answers are very helpful. I'll look into permutations and combinations.
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Re: How many different groups of 3 people can be formed from a group of 5 [#permalink] New post   19 May 2018, 10:01
let assume there are 3 seats and we have 5 people

so for the 1st seat number of options, we have = 5

for the 2nd seat = 4 ( one is already on the 1st seat)
for the 3rd seat = 3 ( two are already on 1st and 2nd)

so total option on 3 seats = 5*4*3 =60 ( we don't need to do the math)
but the question is asking about a group
so how many ways u can sort 3 people = 3! = 3x2 =6 ( so that means we can have 6 arrangements in which we can arrange 3 people )

so \(Total_Groups = \frac{Total Seat Arrangements}{No Of Arragements Per Group} = \frac{60}{6} = 10\)
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Re: How many different groups of 3 people can be formed from a group of 5 [#permalink] New post   05 Dec 2022, 10:40
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: How many different groups of 3 people can be formed from a group of 5 [#permalink]
05 Dec 2022, 10:40
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