Problem #4: A class of 30 students has 16 boys and 14 girls. How many groups of 8...?

[snake1k1]

A class of 30 students has 16 boys and 14 girls. How many groups of 8 students can be formed where

(a) the eldest boy is included in the group?
(b) the eldest boy is excluded from the group?
(c) the eldest boy is excluded if the eldest girl is included (i.e. they can't both be on the committee)

A group of 10 students is now needed to complete 10 different activities. If 5 girls and 5 boys are chosen to do a different activity each. What is the probability:

(d) the eldest boy is chosen to do an activity?
(e) the eldest boy is not chosen to do an activity given that the eldest girl is not chosen to do an activity?

The class of 30 students is now broken into 2 groups, each containing 15 students.

(f) How many ways can the 2 groups be formed
(g) What is the probability that there are 8 boys and 7 girls in each group?

 

[stapel]

A class of 30 students has 16 boys and 14 girls. How many groups of 8 students can be formed where

(a) the eldest boy is included in the group?
(b) the eldest boy is excluded from the group?
(c) the eldest boy is excluded if the eldest girl is included (i.e. they can't both be on the committee)

A group of 10 students is now needed to complete 10 different activities. If 5 girls and 5 boys are chosen to do a different activity each. What is the probability:

(d) the eldest boy is chosen to do an activity?
(e) the eldest boy is not chosen to do an activity given that the eldest girl is not chosen to do an activity?

The class of 30 students is now broken into 2 groups, each containing 15 students.

(f) How many ways can the 2 groups be formed
(g) What is the probability that there are 8 boys and 7 girls in each group?

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck? For instance, for part (a), after reserving one spot for the specified person, there are seven other slots to be chosen, at random, from the remaining fifteen males and fourteen females (or, more specifically, from the other twenty-nine persons). How many total groups of this sort did you get? And so forth.

Please be complete. Thank you! :wink:

 

[snake1k1]

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck? For instance, for part (a), after reserving one spot for the specified person, there are seven other slots to be chosen, at random, from the remaining fifteen males and fourteen females (or, more specifically, from the other twenty-nine persons). How many total groups of this sort did you get? And so forth.

Please be complete. Thank you! :wink:

Need help with pretty much everything.

 

[stapel]

Need help with pretty much everything.

Since you're completely unable to make any start with anything (even plugging numbers into the customary formula), I would suggest that you consider enrolling in an appropriate sequence of courses at your local college or university, leading up to a course in statistics. In that course, they'll cover all of the material necessary to understanding what is being asked of you, and will provide you with the appropriate formulas, tables, methods, and techniques. Have fun!

 

[snake1k1]

Since you're completely unable to make any start with anything (even plugging numbers into the customary formula), I would suggest that you consider enrolling in an appropriate sequence of courses at your local college or university, leading up to a course in statistics. In that course, they'll cover all of the material necessary to understanding what is being asked of you, and will provide you with the appropriate formulas, tables, methods, and techniques. Have fun!

Thanks for the advice. However, still any help figuring out the solution would be very helpful and much appreciated.

 

[stapel]

Thanks for the advice. However, still any help figuring out the solution would be very helpful and much appreciated.

The "help" was the suggestion that you plug the given values into the standard formulas. But since you haven't yet started a course in statistics, you haven't yet seen those formulas.

Are you asking to links, so you can attempt online self-study? If so, do you know anything about "combinations" and "permutations", or are you needing to start at the very beginning? What online-lessons sites have you tried using so far? Thank you!