From a faculty of six professors, six associate professors, ten assistant professors, and twelve instructors, a committee of size six is formed randomly. what is the probability that
(a) there are exactly two professors on the committee;
(b) all committee members are of the same rank

a) 0.23

               b) 0.00085

Step-by-step explanation:

6 professors

6 associate professors,

10 assistant professors,  

12 instructors

Committee: 6 people

Total of combinations possible:

C₃₄,₆ =   34!   = 1344904

           6! 28!

(a) there are exactly two professors on the committee;

C₆,₂ * C₂₈,₄ =   6!   *    28!   = 15*20475 = 307125

                    2! 4!      4! 24!  

P = 307125/1344904 = 0.23

(b) all committee members are of the same rank

All prof: C₆,₆ = 1

All assoc. prof: C₆,₆ = 1

All assist prof: C₁₀,₆ = 210

All instr: C₁₂,₆ = 924

1+1+210+924 = 1136

P = 1136/1344904 = 0.00085

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2