A school had a very unusual tradition involving its 1000 students and its 1000 lockers. On opening day, after the head of the school had closed all the lockers, a student walked by and opened every single one. A second student then closed every second one (#2, 4, 6, 8 etc). A third student then changed every third locker (#3,
How many 5 card poker hands are there? Note a deck of 52 cards is assumed.
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
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
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?
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?
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
Explain combinations, please.
There are two small cities, Santa Clara and Santa Rosa. Santa Clara has 20 houses and Santa Rosa has 15 houses. An inspector must randomly choose 5 houses in Santa Clara and 7 houses in Santa Rosa to inspect. How many different ways can this be done?
How many committees consisting of three men and two women can be formed from seven men and six women?
Car license plates in California take the form of 1RTY345. If zero cannot be used in the first position and repeats are allowed in the other 6 positions, how many license plates are possible?
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
Permutation 89! __________ 80!(89-80)!
A concert to raise money for an economics prize is to consist of 5 works: 2 overtures, 2 sonatas, and a piano concerto. a) In how many ways can the program be arranged? b) In how many ways can the program be arranged if an overture must come first?
Using the numbers 2,7,8, and 9 what is an equation that equals 24?
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
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
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