Sets/Counting

Can you check my answers and help me with the ones that are incorrect? thank you A Hand consists of: 1 card from a 52 flower picutre card deck 1 card from a 52 bird picutre card deck Standard deck (13 cards in 4 sutis:2-10,J,Q,K,A) Note - flower ace of spades, bird queen of hearts and bird ace of spades, flower queen of spades are two differnet outcomes A. How many different hands are possible? 52 * 52 = 2704 B. How many hands consist of a pair of aces? 4 * 4 = 16 C. How many hands contain all face cards 16*16 = 256 D. How many hands consist of two of a kind (two king, two aces....) 4*4 = 16 -> 14 * 16 = 208 E. How many hands contain exactly one king? ... click for more

Using Permutations and Combinations

Can you check my answers and help me with B? Preparing a plate of cookies for 8 children, 3 types cookies {chocolate chip, peanut butter, oatmeal}, unlimited amount of cookies in supply but only cookie per child. One cookie per plate, one plate per child. A) How many different plates can be prepared? C(8,3) = 56 B) How many different plates can be prepared if at least one of each kind of cookie is given out ? C) How many different plates can be prepared if no one likes oatmeal? C(8,2) = 28 D) How many different plates can be prepared if two children need to get peanut butter? C(6,3) = + C(2,1) = 22 E) How many different plates can be prepared if the dog got into the kitche... click for more

Principle Of Inclusion and Exclusion

let IU - intersection U - union Write an expression for the number of terms in the expansion of |A1 U ... U An| given in equ Sum 1<=i

Cannot Work this one

In the questions below suppose the variable x represents students and the variable y represents courses, and A(y): y is an advanced course S(x): x is a sophomore F(x): x is a freshman T(x,y): x is taking y. Write the statement using these predicates and any needed quantifiers. a. There is a course that every freshman is taking. b. Some freshman is taking an advanced course.

I am stumped

This question has three parts: So I am making it 5 credits for that reason. a. Show that the hypotheses "I left my notes in the library or I finished the rough draft of the paper" and "I did not leave my notes in the library or I revised the bibliography" imply that "I finished the rough draft of the paper or I revised the bibliography". b. Using c for "it is cold" and d for "it is dry", write "It is neither cold nor dry" in symbols. c. Show that the premises "Everyone who read the textbook passed the exam", and "Ed read the textbook" imply the conclusion "Ed passed the exam".