The staff of a bank consists of a manager, the deputy manager and other 10 officers. A committee of 4 is to be selected. Find the number of ways in which this can be done so that this can be done so as to always include (i) the manager, (ii) the manager but not the deputy manager, (iii)neither the manager nor the deputy manager.

answer: 8

step-by-step explanation: if you add the possibilities 5 different flavor and 3 different sizes 5+3=8

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0

arc length = radius * x ( in radians)

6 * pi = 18 * x

divide by 18 on each side

6 pi / 18 = x

pi/3 = x

the angle is pi / 3 radians

or   60 degrees