Twenty people work at a small startup. A six-person committee is to be formed.

(a) Let D denote the set of all possible committees. Find |D|.
(b) Two of the workers, Alice and Beth, will be unhappy if they have to serve together. Let P be the set of possible committees with both Alice and Beth. Find |P|.
(c) Beth will also be unhappy if she has to serve with both Frank and Grace. Let Q be the set of possible committees on which Beth, Frank, and Grace would all serve together. Find |Q|.
(d) Find |P ∩ Q|.
(e) Let S be the set of all possible committees on which there is at least
one unhappy employee. Express S in terms of only P and Q.
(f) Find |S|.
(g) How many committees can we form with no unhappy employees?
(h) Instead of one committee, we decide to form two six-person commit- tees. Each employee can be on at most one committee. How many ways can we form these committees, if employee happiness is nottaken into consideration?

step-by-step explanation:

1

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

a natural event such as a flood, earthquake, or hurricane that causes great damage or loss of life.

step-by-step explanation: