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

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Math Expert
Joined: 02 Sep 2009
Posts: 58092
A committee of 2 people is to be selected out of 3 teachers and 4 prea  [#permalink]

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03 Oct 2016, 23:24
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:41) correct 19% (01:56) wrong based on 93 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

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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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04 Oct 2016, 03:29
1
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

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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01 Dec 2017, 07:45
1
2
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.

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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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29 Nov 2017, 06:15
Can any one explain better why is the D the result ? i just thought it would be prob=4C1*4C2/7C2

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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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07 Aug 2019, 02:59
Bit late here, but think my solution will add up to the above ;Incase,you still don’t understand

P(at least 1 preacher) + P(no preacher) =1
.: P(at least 1preacher) =
1 - P(no preacher)

So P(no preacher ) = 3C2/7C2 =1/7

It’s 3C2 because we have 3 teachers who are not preachers of which we select 2
Divided by 7people of which we select 2 ...Got it

Now, P(at least 1 preacher) = 1-1/7
P(at least 1 preacher) = 6/7

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A committee of 2 people is to be selected out of 3 teachers and 4 prea   [#permalink] 07 Aug 2019, 02:59
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