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Magazine Problem 1
List all partitions of the set \(A=\\{a, b, c\\}\).
Problem 2
Professor Shortcut records his grades using only his students' first and last initials. What is the smallest class size that will definitely force Prof. S. to use a different system?
Problem 2
(a) How many three-digit numbers can be formed from the digits \(1,2,\) 3 if no repetition of digits is allowed? List the three-digit numbers. (b) How many two-digit numbers can be formed if no repetition of digits is allowed? List them. (c) How many two-digit numbers can be obtained if repetition is allowed?
Problem 3
How many subsets of \(\\{1,2,3, \ldots, 10\\}\) contain at least seven elements?
Problem 4
The congressional committees on mathematics and computer science are made up of five representatives each, and a congressional rule is that the two committees must be disjoint. If there are 385 members of congress, how many ways could the committees be selected?
Problem 6
(a) A group of 30 students were surveyed and it was found that 18 of them took Calculus and 12 took Physics. If all students took at least one course, how many took both Calculus and Physics? Illustrate using a Venn diagram. (b) What is the answer to the question in part (a) if five students did not take either of the two courses? Illustrate using a Venn diagram.
