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From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?

A. 3/7 B. 5/12 C. 27/70 D. 2/7 E. 9/35

The probability that we’re looking for can be expressed as a follows:

# ways the group can be selected with Andrew but not Karen/total # of ways to select the group

Let’s begin with the numerator. If Andrew makes the team but Karen does not, we can mentally remove Andrew and Karen from the pool of people available for the group. This leaves 6 people available for the full 3 spots (remember Andrew must be selected). 3 people can be chosen from a group of 6 people in 6C3 ways:

(6 x 5 x 4)/3! = 20 ways

For the denominator, we’re looking for the total number of ways in which the 4-person team can be made. The team can be made in 8C4 ways or:

(8 x 7 x 6 x 5)/4! = 70 ways

Thus, the probability that Andrew is selected for the group but Karen is not is 20/70 = 2/7.

Answer: D
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

Definitely not my strong area but need to understand conceptually why this is wrong.

for andrew to be included - 8C1 For the rest three positions left 6C3

why is the 8C1 not required?

There are not 8 ways to choose Andrew. The probability of choosing Andrew out of 8 people is 1/8 but the number of ways to choose Andrew is 1 (1 out of 1 Andrew)..
_________________

Re: From a group of 8 volunteers, including Andrew and Karen [#permalink]

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30 Oct 2016, 06:28

From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not? A. 3/7 B. 5/12 C. 27/70 D. 2/7 E. 9/35

Ans:-

A: Number of ways to select any 4 volunteers at random= 8C4 B: Number of Ways to Select Andrew= 1C1

Now that we have selected 1 volunteer, only 3 more volunteers are to be selected from a lot of 6 volunteers. [i.e. 8-1(Andrew)-1(Karen)=6volunteers] C: Number of ways to select 4 Volunteers including Andrew but not Karen= 1C1*6C3= 6C3

Re: From a group of 8 volunteers, including Andrew and Karen [#permalink]

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13 Jan 2017, 10:47

[Andrew's chances of being selected: 4/8 If Andrew is selected, Karen's chances of not being selected: 4/7 (4/8) * (4/7) = 16/56 or 2/7 quote][/quote]

I solved this question in exactly the same way as decadecaf did (quoted above, sorry if it went wrong, first time quoting, new to GMAT club). Is this method incorrect and simply a result of luck that I achieved the correct answer using this method?

Theory states that NOT questions and AT LEAST questions can be solved using complementary probability, I just want to know whether or not it is vital to use the combination methods to achieve the correct answer in this question.

Re: From a group of 8 volunteers, including Andrew and Karen [#permalink]

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22 Jul 2017, 18:32

mba1382 wrote:

From a group of 8 volunteers, including Andrew and Karen, 4 people are to be selected at random to organize a charity event. What is the probability that Andrew will be among the 4 volunteers selected and Karen will not?

Considering that Andrew will be there , we need to select 3 other people from 6 remaining volunteers excluding Karen.

=> 6C3 / 7C3 = 4/7.

Although finally I randomly guessed and selected correct answer i.e. 2/7, I was not able to get the answer with my approach mentioned here.

Could someone tell me what am I missing here?

In this case, we can start by finding the total number of choices: 8C4 = 8*7*6*5*4*3*2/4*3*2*4*3*2 = 14*5 = 70 choices.

The number of choices of a group with Andrew and without Karen is 6C3 because Andrew is already in the group (so we're down to 7 choices) and Karen is not in the group at all (so we're now down to 6 volunteers). We also deduct one from the choice (from 4 to 3) because Andrew has already been selected. 6C3 = 6*5*4*3*2/3*2*3*2 = 20.