Four sophomores, five juniors and six seniors have volunteered to serve on a committee consisting of...

80.2K

Verified Solution

Question

Advance Math

Four sophomores, five juniors and six seniors have volunteeredto serve on a committee consisting of five people. In how many wayscan the membership of the committee be selected under the followingrestrictions respectively?
(a) Any of the volunteers can serve on the committee.
(b) Only seniors can serve on the committee.
(c) At least one senior must serve on the committee.
(d) At least two juniors and at least two seniors must serve onthe committee.
(e) At least one person from each class must serve on thecommittee, but no more than two members of the same class can serveon the committee.

Answer & Explanation Solved by verified expert

4.4 Ratings (932 Votes)

a Since any of the volunteers can serve on the committee hence the number of ways of selecting the committee membership is the number of ways of selecting any 5 students from the collection of all students The total number of students 456 15 Thus the required number of ways is 15C5 b Since only seniors can serve on the committee hence the number of ways of selecting the committee membership is the number of ways of selecting 5 students from the collection of 6 senior students Thus the required See Answer

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member