Problem Solving

Attorneys are questioning 11 potential jurors about their ability to serve on a jury and decide a case fairly. Seven individuals will be selected to serve on the jury. If each potential juror has an equal chance of being selected, what is the probability that Tamara and Inga are chosen for the jury?
2/11

2/7

21/55

4/11

34/55


I got the answer as 4/11 which is a wrong answer. However this is how I got 4/11:

Total Combination : 11C7 = 330

Combinations where the two will be together : 10C7 = 120

So probability where the two will be together is = 120/330

= 4/11

Plz help me get the right answer.......

This topic tends to be a little annoying at the start. After rigorous practice it becomes relatively smooth.

Your 1st part is correct. 11C7=330
Which is the number of ways to select 7 ppl out of the 11 potential candidates.

Now, the number of selections where both will be included...Well, lets split that up in two parts
Out of the two, we need both to be selected which can happen in 2C2 ways. (2C2=1 but included that here so it would be easy to understand the concept)

Now, there are 5 seats still left and 9 ppl to choose from. So we select these 5 ppl from the 9 in
9C5 ways. Which is 165.

Combining both we get 2C2*9C5=165

165/330=21/55. Hence C

knight247 wrote:This topic tends to be a little annoying at the start. After rigorous practice it becomes relatively smooth.

Your 1st part is correct. 11C7=330
Which is the number of ways to select 7 ppl out of the 11 potential candidates.

Now, the number of selections where both will be included...Well, lets split that up in two parts
Out of the two, we need both to be selected which can happen in 2C2 ways. (2C2=1 but included that here so it would be easy to understand the concept)

Now, there are 5 seats still left and 9 ppl to choose from. So we select these 5 ppl from the 9 in
9C5 ways. Which is 165.

Combining both we get 2C2*9C5=165

165/330=21/55. Hence C

9C5 = 126..How did you get that answer?

2C2*9C5/11C7=21/55

leonswati wrote:Attorneys are questioning 11 potential jurors about their ability to serve on a jury and decide a case fairly. Seven individuals will be selected to serve on the jury. If each potential juror has an equal chance of being selected, what is the probability that Tamara and Inga are chosen for the jury?
A) 2/11
B) 2/7
C) 21/55
D) 4/11
E) 34/55

$$?\,\, = \,\,{{C\left( {11 - 2\,,\,7 - 2} \right)} \over {C\left( {11,7} \right)}}\,\,\mathop = \limits^{\left( * \right)} \,\,{{9 \cdot 7 \cdot 2} \over {11 \cdot 10 \cdot 3}}\,\, = \,\,{{3 \cdot 7} \over {11 \cdot 5}}\,\, = {{21} \over {55}}$$
$$\left( * \right)\,\,\,\left\{ \matrix{
\,C\left( {9,5} \right) = {{9 \cdot 8 \cdot 7 \cdot 6} \over {4 \cdot 3 \cdot 2}} = 9 \cdot 7 \cdot 2 \hfill \cr
\,C\left( {11,7} \right) = {{11 \cdot 10 \cdot 9 \cdot 8} \over {4 \cdot 3 \cdot 2}} = 11 \cdot 10 \cdot 3 \hfill \cr} \right.$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.