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

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)

damm bro the struggle

step-by-step explanation: