3. In a shop there are 10 different types of candies. How many ways are there...
1. A state legislature consists of 7 Democrats, 4 Republicans, and 8 Independents. How many ways are there to choose: a. A committee of 5 legislators? b. A speaker, a vice-speaker, and a sergeant at arms? c. A committee of 6 legislators where 2 are Republicans, and 2 are Democrats, and 2 are Independents? d. A committee of 5 legislators, with no Independents? 2. A "2 for $20" meal deal at a local restaurant allows you to pick 1 appetizer...
q) A camera shop stocks eight different types of batteries, one of which is type A7b. Assume there are at least 30 batteries of each type. a. How many ways can a total inventory of 30 batteries be distributed among the eight different types?
(A) How many different ways are there for 17 of the 24 people to develop the disease? (B) Now suppose 9 of the 24 people carry a specific genetic mutation, and 5 of those are in the group that develops the disease. How many different ways are there for this to happen?
5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every child gets at least one chocolate? (b) In how many ways can we distribute 5 different chocolates to 9 children so that every child gets at most one chocolate? 5) (a) In how many ways can we distribute 10 different chocolates to 4 children so that every child gets at least one chocolate? (b) In how many ways can we distribute 5...
You have 6 friends. How many ways are there to invite a different subset of two of these friends over for dinner on 4 successive nights? (A friend might be invited more than once; just the subset of 2 friends must be different each night.) \ ANSWER: P(C(6,2)4)
How many ways are there to select 8 donuts from 6 types of donuts if at most 3 donuts are chosen from the first two types combined; that is, at least 5 donuts chosen from the other four types. (Hint: break into cases) answer: break into 4 cases for 0 or 1 or 2 or 3 in first two boxes sum for i from 0 to 3 {C(2+i-1,i)xC(4+(8-i)-1,(8-i))};
3. Suppose my graph theory class has 12 different students, of which 6 are under- grads and 6 are graduate students. (a). How many ways can I choose at least 4 but no more than 8 of my students to take a field trip to the library? (b). I want to repeat part (a), but I want to be sure to take at least 2 undergrads. (c). I have 3 different final projects for them to work on (projects A,...
10) 6. True or False: IR is used to tell how many chemically different types of hydrogens F T a. T F CDCI, is commonly used as an NMR solvent. b. T F Compounds with no nitrogen always have an even mass number. C. d. Aldehydes are easy to detect in HNMR. T F Neighboring hydrogens always show spin-spin splitting. T F e.
Please answer the following question: a) In how many ways can a committee of 3 people be selected from a group of 10 people? b) In how many ways (different arrangements) can 8 books be placed on a shelf? c) On an ice cream menu, there are 5 choices of ice cream flavors, 4 choices of toppings and 2 choices of syrups. In how many different ways can the ice cream be ordered, if each order must include one ice...
3. Six if the bag three types. friends share a bag of assorted donuts. How many ways can they share the donuts g contains (A) six different donuts, (B) three each of two types, (C) two each of 4. From a standard deck of cards, what are the odds against drawing (A) a face card, (B) two face cards?