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Waterbury Hall, a university residence hall for men, is operated under the supervision of Mr. Kelly. The residence has three floors, each of which is divided into four sections. This coming fall Mr. Kelly will have 12 resident assistants (one for each of the 12 sections). Among these 12 assistants are the four senior assistants - Mr. DiRocco, Mr. Fairbanks, Mr. Hyland, and Mr. Thornhill. (The other eight assistants will be new this fall and are designated as junior assistants.) In how many ways can Mr. Kelly assign his 12 assistants if
(a) There are no restrictions?
(b) Mr. DiRocco and Mr. Fairbanks must both be assigned to the first floor?
(c) Mr. Hyland and Mr. Thornhill must be assigned to different floors? |
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