toys of the same material type must be grouped together;(B)rubber toys should not be next to each other?
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In how many ways can 3 paper toys, 7 rubber toys, and 5 plastic toysbe arranged in a row if:(A)toys of the same material type must be grouped together;(B)rubber toys should not be next to each other?
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- 1. Dr. Orchid has 9 paintings she wants to hang side by side on her wall. (a) In how many ways can she arrange all 9 paintings? Show your work. (b) If she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.Suppose there are 5 men and 8 women qualified to be members of a new committee of 6 people, includinga president, a vice-president, and a secretary.(a) How many different ways do you have to pick a president, vice-president and secretary if you need atleast 1 men and 1 women? Does the order matter? Why?(b) How many different committees can you form with at least 3 women? Does the order matter? Why?Your professor has 10 advanced statistics texts and 8 advanced calculus texts. (a) How many ways can the 10 statistics texts be arranged on the top shelf?(b) How many ways can the 8 calculus texts be arranged on the bottom shelf?(c) How many ways can the 18 texts be arranged together on a single shelf, with the statistics texts grouped together and the calculus texts grouped together?
- (a) Of the 7 new programmers hired by a software company, 4 will work on web applications, 2 will work on desktop applications, and 1 will work on mobile applications. In how many ways can this arrangement be made? (b) Answer the same question if 8 programmers are hired (some of them will not be assigned to any task yet).A newly established company needs to have a committee that consists of one accountant, two marketing agents, and four board members. If there are four accountants, three marketing agents, and eight board members available for selection in the committee, in how many ways can the committee be formed? /3APP BA contractor builds homes of 11 different models and presently has 6 lots to build on. In how many different ways can he arrange homes on these lots? Assume 6 different models will be built.
- Suppose we want to choose 4 objects, without replacement, from 17 distinct objects. (a) If the order of the choices is not relevant, how many ways can this be done? (b) If the order of the choices is relevant, how many ways can this be done?Suppose we want to choose 5 objects, without replacement, from 9 distinct objects. (a) If the order of the choices is not taken into consideration, how many ways can this be done? (b) If the order of the choices is taken into consideration, how many ways can this be done?6. Mai is arranging 12 cans of food in a row on a shelf. She has 8 cans of beets, 3 cans of beans, and 1 Canof olives. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)? Answer:
- Suppose there are 6 girls and 6 boys in a class. In how many ways can you arrange these children in a row if two of the girts are frends and mut st ret ah other?Five electrical engineering books, seven electronics engineering books, and eight civil engineering books are to be arranged in a shelf. In how many ways can you arrange all the books in a row? b. In how many ways can you arrange the books in a row in such a way that books for each engineering major are always adjacent to one another. а.2. I found some bingo cards in our classroom. A bingo card seems to have 5 rows and 5 columns. The center cell is blank, but the remaining cells each contain a number. No two cells contain the same number. In the first column, integers from 1 to 15 are used. In the 2nd column, integers from 16 to 30 are used, and so on. Thus, in the 5th column, integers from 61 to 75 are used. How many different bingo cards are there? Explain.
