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

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Intern
Joined: 06 Oct 2010
Posts: 40

Kudos [?]: 24 [0], given: 29

How many different groups of 3 people can be formed from a [#permalink]

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10 Oct 2010, 14:19
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:14) correct 8% (00:23) wrong based on 125 sessions

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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
[Reveal] Spoiler: OA

Kudos [?]: 24 [0], given: 29

Retired Moderator
Joined: 02 Sep 2010
Posts: 793

Kudos [?]: 1186 [1], given: 25

Location: London
Re: Is there a faster way to solve this problem? [#permalink]

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10 Oct 2010, 14:23
1
KUDOS
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
[Reveal] 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.

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.
_________________

Kudos [?]: 1186 [1], given: 25

Math Expert
Joined: 02 Sep 2009
Posts: 41888

Kudos [?]: 129208 [1], given: 12196

Re: Is there a faster way to solve this problem? [#permalink]

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10 Oct 2010, 14:25
1
KUDOS
Expert's post
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
[Reveal] 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.

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 $$C^3_5=\frac{5!}{3!(5-3)!}=10$$.

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

Hope it helps.
_________________

Kudos [?]: 129208 [1], given: 12196

Intern
Joined: 06 Oct 2010
Posts: 40

Kudos [?]: 24 [0], given: 29

Re: Is there a faster way to solve this problem? [#permalink]

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10 Oct 2010, 22:12

Kudos [?]: 24 [0], given: 29

Intern
Joined: 25 Apr 2012
Posts: 1

Kudos [?]: [0], given: 0

How many different groups of 3... [#permalink]

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24 May 2012, 15:15
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

Kudos [?]: [0], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41888

Kudos [?]: 129208 [0], given: 12196

Re: How many different groups of 3... [#permalink]

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24 May 2012, 15:20
Tommytran80 wrote:
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

Merging similar topics. Please refer to the solution above.
_________________

Kudos [?]: 129208 [0], given: 12196

Re: How many different groups of 3...   [#permalink] 24 May 2012, 15:20
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