question archive 2) Eight students-Abdul, Bilal, Charles, Daria, Emma, Filip, Gabriella, and Hao-meet over Zoom to delegate tasks for a final group project
2) Eight students-Abdul, Bilal, Charles, Daria, Emma, Filip, Gabriella, and Hao-meet over Zoom to delegate tasks for a final group project
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2) Eight students-Abdul, Bilal, Charles, Daria, Emma, Filip, Gabriella, and Hao-meet over Zoom to delegate tasks for a final group project. (i) They decide to put three people in charge of research, two people to write the final report, and three to make slides and present in class. How many ways can they delegate tasks among the group members? (ii) Emma volunteers to work on the written report, while Daria and Gabriella, being roommates, insist on working on the same task. How many ways can they delegate tasks among the group members?
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- First choose the people for research. Since there are 8 people for this task, there are (8 choose 3) = 56 ways to do this. Then choose 2 people for writing. There are 5 people left, so there are (5 choose 2) = 10 ways to do this. The remaining 3 are on presentation. Thus the total is 56*10 = 560.
- With Emma doing written, there 7 people to split into groups of 3, 1, and 3. Then Daria and Gabriella go together in one of the 3 person groups, so there are 2 choices for that. This leaves us with (1, 1, 3) or (3, 1, 1) with 5 more people. Thus there are (5 choose 3) = 10 ways to fill the three person group and 2 ways to fill one of the one person groups, leaving exactly one person to fill the other group. Thus the total is 2*10*2 = 40
