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Combinatorics

Permutation and Combination

For each new employee, a company gives a five-digit identification card. Each digit can be 0, 1, 2, or 3. If repetitions are allowed, how many different cards are possible. A. 1024 B. 625 C. 25 D. 500

Permutation -Combination

An anthropologist discovers an isolated tribe whose written alphabet contains only six letters called a, b, c, d, e, and f. The same letters cannot be used twice in the same word. If each different sequence of letters constitutes a different word in the language, what is the maximum number of six-letter words that the language

Working with combinations to select a baseball team.

The coach of the Morton Valley Softball Team has 6 good hitters and 8 poor hitters. He chooses 3 hitters at random. (a) In how many ways can he choose 2 good hitters and 1 poor hitter? (b) In how many ways can he choose 3 good hitters? (c) In how many ways can he choose at least 2 good hitters?

Working with permutations and combinations.

If the number of permutations of n objects taken r at a time is six times the number of combinations of n objects taken r at a time, determine the value of r. Is there enough information to determine the value of n? Why or why not?

Permutation, combination, probability

1. How many ways are there to choose 5 items (with repetition) from among 7 varieties? Explain, as precisely as possible, why we should not factor out by the number of arrangements of the 5 choices. ( Don't prove that the answer is wrong-we already did that- explain why it's wrong, i.e., why we shouldn't factor out by r!) It mig

Finding the maximum numbers of ways to arrange a word.

An anthropologist discovers an isolated tribe who has written an alphabet that contains only six letters (call the letters A, B, C, D, E, and F). The tribe has a taboo against using the same letter twice in the same word, it's never done. If each different sequence of letters constitutes a different word in the language, what is

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