Find: (a) A' UB' (b) A' NB' (c) (A UB)'
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- The Department of Mathematics of a certain university in a recent survey was found to consist of 80 faculty members. The survey also revealed the information that among them, there are: 40 male professors; 38 married professors; 26 professors with more than 10 years of service; 15 married male professors; 14 married professors with more than 10 years of service; 13 male professors with more than 10 years of service; and 6 married male professors with more than 10 years of service. How many unmarried female professors have less than or equal to 10 years of service?Suppose there are 10 students participating in a workshop that meets every day of a five-day work week. Each student must present a poster in exactly one of the days of the workshop, and every day of the workshop should have at least one poster presentation. If nk denotes the number of posters presented in day k of the workshop, what is the number of possible quintuples (n1,n2,n3,n4,n5)? I ll rate accordingly.Suppose u=⟨−4,4,−2⟩ and v=⟨4,−2,3⟩. Then u×v= v×u=
- If A={f,i,l,m,o,g,r,a,p,h,y}A={f,i,l,m,o,g,r,a,p,h,y} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′A′.Individual A has a circle of five close friends (B, C, D,E, and F). A has heard a certain rumor from outside thecircle and has invited the five friends to a party to circulatethe rumor. To begin, A selects one of the five atrandom and tells the rumor to the chosen individual.That individual then selects at random one of the fourremaining individuals and repeats the rumor. Continuing,a new individual is selected from those not already havingheard the rumor by the individual who has just heardit, until everyone has been told.a. What is the probability that the rumor is repeated inthe order B, C, D, E, and F?b. What is the probability that F is the third person atthe party to be told the rumor?c. What is the probability that F is the last person tohear the rumor?d. If at each stage the person who currently “has” therumor does not know who has already heard it andselects the next recipient at random from all fivepossible individuals, what is the probability that Fhas still not heard the…Construct a Venn Diagram for the scenario. Suppose that a total of 208 students are enrolled in a Math course which offers three classes under Instructor X, Instructor Y, and Instructor Z. 4 students are enrolled under all three instructors. 48 students are enrolled under Instructor. Y. Twice as many students are enrolled under Instructor Y and Z (but not Instructor X) as those who are enrolled under both Instructor Y and X (but not Instructor Z), and 4 times as many as those enrolled under all three instructors. 124 students are enrolled in Instructor Z. 27 students are not enrolled in any class. Students enrolled under both Instructor Y and Z (but not Instructor X) is exactly the same size as the students enrolled under both Instructor X and Z.
- Assume that you have 6 red balls and 10 blue balls from which randomly to select two without replacementThere are 200 individuals with a skin disorder, 120 had been exposed tothe chemical C1, 50 to chemical C2, and 30 to both the chemicals C1 and C2. Find the number of individuals exposed to(i) Chemical C1but not chemical C2(ii) Chemical C2 but not chemical C1(iii) Chemical C1or chemical C2I have a bucket of n green balls labeled 1, 2, . . . , n. I have another bucket of red ballslabeled 1, 2, . . . , m. How many combinations of five green balls and three red balls canI draw from these buckets?
