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A committee of 2 people is to be selected out of 3 teachers and 4 prea

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A committee of 2 people is to be selected out of 3 teachers and 4 prea [#permalink]

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New post 03 Oct 2016, 22:24
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (01:23) correct 21% (01:26) wrong based on 66 sessions

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A committee of 2 people is to be selected out of 3 teachers and 4 preachers. If the committee is selected at random, what is the probability that the committee will be composed of at least 1 preacher?

A. 1/4
B. 1/3
C. 2/3
D. 6/7
E. 8/9
[Reveal] Spoiler: OA

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Kudos [?]: 135981 [0], given: 12719

Senior Manager
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Joined: 06 Jun 2016
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Location: India
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Re: A committee of 2 people is to be selected out of 3 teachers and 4 prea [#permalink]

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New post 04 Oct 2016, 02:29
Bunuel wrote:
A committee of 2 people is to be selected out of 3 teachers and 4 preachers. If the committee is selected at random, what is the probability that the committee will be composed of at least 1 preacher?

A. 1/4
B. 1/3
C. 2/3
D. 6/7
E. 8/9



Answer D
Total no of ways in which you can select a committee of 2 people out of 7 people is 7C2 ways= 21 ways
Requirement is at-least 1 preacher= 4C1*3C1+4C2 or 7C2-3C2=18 ways
Probability= 18/21 = 6/7

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Re: A committee of 2 people is to be selected out of 3 teachers and 4 prea [#permalink]

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New post 29 Nov 2017, 05:15
Can any one explain better why is the D the result ? i just thought it would be prob=4C1*4C2/7C2

Thx in advance

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Re: A committee of 2 people is to be selected out of 3 teachers and 4 prea [#permalink]

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New post 01 Dec 2017, 06:45
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Bunuel wrote:
A committee of 2 people is to be selected out of 3 teachers and 4 preachers. If the committee is selected at random, what is the probability that the committee will be composed of at least 1 preacher?

A. 1/4
B. 1/3
C. 2/3
D. 6/7
E. 8/9



To determine how many ways to select at least one preacher, we can use the formula:

Number of ways to select at least 1 preacher = total number of ways to select the group - number of ways to select NO preachers

Total number of ways to select the group is:

7C2 = 7!/[2!(7-2)!] = (7 x 6)/2! = 21

The number of ways to select NO preachers is:

3C2 = (3 x 2)/2! = 3

Thus, the number of ways to select at least 1 preacher is 21 - 3 = 18 ways.

So the probability that the committee will be composed of at least 1 preacher is 18/21 = 6/7.

Answer: D
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Kudos [?]: 1024 [1], given: 3

Re: A committee of 2 people is to be selected out of 3 teachers and 4 prea   [#permalink] 01 Dec 2017, 06:45
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