Seven people (A,B,C,D,E, F, and G) are seated in a row. Suppose A,B, and C are...

Seven people (A,B,C,D,E, F, and G) are seated in a row. Suppose A,B, and
C are freshmen, D and E are sophomores and F and G are juniors. How many
arrangements are possible if:
(a) D and F must sit together?
(b) A and C must not sit together?
(c) All freshmen must sit together?
(d) All freshmen must sit together, all sophomores must sit together, and all
juniors must sit together?
(e) Exactly two people sit between A and B?

Expert Solution

orchestra answered 1 year ago

Five persons A, B, C, D, and E are seated at random in a row of...

Five persons A, B, C, D, and E are seated at random in a row of seats numbered 1, 2, 3, 4, and 5. a) Find the probability that A is seated on seat 2. b) FInd the probability that A and B are not seated with each other.

In how many ways can 7 people { A, B, C, D, E, F, G }...

In how many ways can 7 people { A, B, C, D, E, F, G } be seated at a round table if (a) A and B must not sit next to each other; (b) C, D, and E must sit together (i.e., no other person can sit between any of these three)? (c) A and B must sit together, but neither can be seated next to C or D. Consider each of these separately. For (c) you may NOT...

In how many ways can 9 people { A, B, C, D, E, F, G, H,...

In how many ways can 9 people { A, B, C, D, E, F, G, H, I } be seated at a round table if (A) A and B must not sit next to each other; (B) C, D, and E must sit together? (C) A and B must sit together, but neither can be seated next to C, D, or E. Consider each of these separately. For (C) you may NOT simply list all possibilities, but must use the...

One five-member committee consists of individuals A,B,C,D,E seated in a straight row from left to right....

One five-member committee consists of individuals A,B,C,D,E seated in a straight row from left to right. How many distinct seating arrangements are possible? If E is seated far left, how many distinct seating arrangements are possible? If B is seated far right, how many distinct seating arrangements are possible? If A is seated in the center, how many distinct seating arrangements are possible? If C and D are far left and far right respectively, how many distinct seating arrangements are...

If there are 7 total notes C, D, E, F, G, A, and B and if...

If there are 7 total notes C, D, E, F, G, A, and B and if a five-note melody is selected at random (so that all melodies counted in part (a) are equally likely to be chosen), what is the probability that the melody will include exactly two “A” notes, but no other repeated notes? (A few allowable examples: AACEG, ACAEG, DFACA, EAABC, etc.)

(a) (f ∘ g)(3) (b) g(f(2)) (c) g(f(5)) (d) (f ∘ g)(−3) (e) (g ∘ f)(−1) (f) f(g(−1))

A restaurant has dishes A, B, C, D, E, F and G The owners anticipate that...

A restaurant has dishes A, B, C, D, E, F and G The owners anticipate that dishes will be ordered in the following proportions: 30% (A), 15% (B), 20% (C), 5% (D), 8% (E), 12% (F) and 10% (G). The number of orders placed during the first two days of business was 75 (A), 60 (B), 50 (C), 14 (D), 20 (E), 40 (F), and 41 (G). State and conduct the appropriate hypothesis test to determine whether there is...

Consider the relation R= {A, B, C, D, E, F, G, H} and the set of...

Consider the relation R= {A, B, C, D, E, F, G, H} and the set of functional dependencies: FD= {{B}—> {A}, {G}—> {D, H}, {C, H}—> {E}, {B, D}—> {F}, {D}—>{C}, {C}—> {G}} 1) Draw FD using the diagrammatic notation. 2) What are all candidate keys for R? 3) If delete {C}—>{G} and change {C, H}—> {E} to {C, H}—> {E, G}, what are all candidate keys for R

Six people (A, B, C, D, E, F) are lining up to enter a museum. (1)...

Six people (A, B, C, D, E, F) are lining up to enter a museum. (1) How many ways are there to line up the six people if A is somewhere before B, although not necessarily immediately before? (2) How many ways are there to line up the six people if A is next to C? (3) How many ways are there to line up the six people if A must be next to B but C and D can...

Consider the cross: A/a; b/b; C/c; D/d; E/e x A/a; B/b; c/c; D/d; e/e a) what...

Consider the cross: A/a; b/b; C/c; D/d; E/e x A/a; B/b; c/c; D/d; e/e a) what proportion of the progeny will phenotypically resemble the first parent? b) what proportion of the progeny will genotypically resemble neither parent?

Question