Alan and Becky are among the ten students a teacher can choose from to

Question

Alan and Becky are among the ten students a teacher can choose from to form a six-student team. If all six students are chosen at random, what is the probability of choosing a team that includes Alan and Becky?

A. 1/9
B. 1/6
C. 2/9
D. 5/18
E. 1/3

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Official Answer

E

A. 1/9
B. 1/6
C. 2/9
D. 5/18
E. 1/3

Are You Up For the Challenge: 700 Level Questions

Nidzo · Answer

\frac{8}{10}+\frac{7}{9}+\frac{6}{8}+\frac{5}{7}+\frac{2}{6}+\frac{1}{5} = \frac{1}{45}

However, in doing this I have created a specific order and found the probability of choosing four students and then either Alan and Becky as the last two. To rectify this, I must multiply  \frac{1}{45}  by  \frac{6!}{4!2!} = 15

\frac{1}{45} * 15 = \frac{15}{45} = \frac{1}{3}

Answer E.

ashishj4 · Answer

Solution=>  
Total ways of choosing any team of 6-student team from 10 available students = 10C6 (order of choosing is not important)

Now we are asked to find the probability of choosing a team that includes Alan and Becky,

Lets suppose we have Alan and Becky in a team, now there are 4 positions remaining for that team and 8 students to choose from,
=> we can choose 4 students from a group of 8 in 8C4 ways

Therefore P(team with Alan and Becky) = Ways of choosing team with Alan and Becky/ Total ways of choosing the team
=> 8C4/10C6 = 1/3

JeffTargetTestPrep · Answer

probability = favorable/total

The total number of outcomes can be determined with the combination formula:

total = 10C6 = 10!/(6!4!) = 210

The number of favorable outcomes also can be determined with the combination formula, but we must consider the fact that, if Alan and Becky must be on the team, then it’s already decided that they are on the team. The teacher can change the team only by choosing a different combination of 6 – 2 = 4 students from the other 10 – 2 = 8 students.

favorable = 8C4 = 8!/(4!4!) = 70

So,

probability = 70/210 = 1/3

Answer: E

Paras96 · Answer

Probability = No. of favorable outcomes / No. of total outcomes = 8C4/10C6 = 70/210=1/3

Hence E

Alan and Becky are among the ten students a teacher can choose from to

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