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Combinatorics

Working with combinations.

An admission test given by a university contains 10 true-false questions. Eight or more of the questions must be answered correctly in order to be admitted. (a) How many different ways can the answer sheet be filled out? (b) How many different ways can the answer sheet be filled out so that 8 or more questions are answer

Working with sequential ambiguity.

In a specific sequence to create, a1 has the elements x1 and y1, a2 has the elements x2 and y2, a3 has the elements x3 and y3, The relationship between each term cannot be bijective, however it has a bounded range of finite whole numbers. Create a rule such that f(x1,y2)=x2 and f(x2,y3) = x3. The rule must be su

Setting up constraints.

How do I set up the contraints? A firm is engaged in the production of three types of products A, B, and C. The products earn profit of $3, $5 and $4 per unit respectively. Each product goes through three operations: cutting, sewing, and inspection. During the next period, the firm has 300 hours of cutting, 300 hours of se